This question can be answered into two aspects:
1) Why is Linga form worshipped ?
2) Why is Shiva primarily worshipped in Linga form ?
1) Why is Linga form worshipped ?
Among the 18 major Mahapuranas one of the Purana is named Linga Purana, thus glorifying the status of Linga.
Linga is worshipped because Linga contains everything of this world. In the Linga Purana [part 2 chapter 46], once sages have debate regarding why Linga form is worshipped. Then Goddess Saraswati comes there and states this fact:
अथांतरिक्षे विपुला साक्षाद्देवी सरस्वती ।
अलं मुनीनां प्रश्नोऽयमिति वाचा बभूव ह ।।
सर्वं लिंगमयं लोकं सर्वं लिंगे प्रतिष्ठितम् ।
तस्मात्सर्वं परित्यज्य स्थापयेत्पूजयेच्च तत् ।।
May the questions of the sages stop. The whole world is identical with the Linga. Everything is found on the Linga. Hence, one shall eschew everything, install the Linga and worship it.
Goddess Saraswati also states all Gods are situated in a Linga. She states:
स्वेषुस्वेषु च पक्षेषु प्रदानास्ते यथा द्विजाः |
ब्रह्मा हरश्च भगवान्विष्णुर्देवी रमा धरा ।।
लक्ष्मीर्धृति: स्मृति: प्रज्ञा धरा दुर्गा शची तथा ।
रुद्राश्च वसव: स्कन्दो विशाख: शाख यव च ।।
नैगमेशश्च भगवाँल्लोकपाला ग्रहास्तथा ।
सर्वे नंदिपुरोगाश्च गणा गणपति: प्रभु: ।।
पितरो मुनय: सर्वे कुबेराद्याश्च सुप्रभा: ।
आदित्या वसव: सांख्या अश्चिनौ च भिषग्वरौ ।।
विश्वेदेवाश्व साध्याश्च पशव: पक्षिणों मृगा:।
ब्रह्मादिस्थावरांतं च सर्वं लिंगे प्रतिष्ठितम् ।।
तस्मात्सर्वं परित्यज्य स्थापयेल्लिंगमव्ययम् ।
यत्नेन स्थापितं सर्वं पूजितं पूजयेद्यदि ।।
All the deities like Brahma, śiva, Earth, Lakshmi, dhṛti, smṛti, prajñā, durgā, śacī, Rudra, Vasu, Skanda, viśākha, śākha, naigameśa, dikapalakās(guardians of the directions), the planets, gaṇās, nandī, Ganapati, pitṛ gaṇās, ṛṣis , kubera, āditya, sāṃkhya, aśvinīkumārās- the best of the physicians, viśvadevās, sādhyās , paśus, birds and animals, besides all the mobile and immobiles, starting from Brahma are established in the linga. Therefore, leaving aside everything, linga should be consecrated. After consecrating it with all the efforts, incase, one adores the shivalinga, then he gets adorable by all.
Thus as every Gods are situated in Linga it is highly auspicious to worship Linga. Trinities are situated in Linga and it is also stated in the next chapter ie. [Part 2 chapter 47] of Linga Purana:
मूले ब्रह्मा वसति भगवान्मध्यभागे च विष्णु: ।
सर्वेशानः पशुपतिरजो रुद्रमूर्तिर्वरेण्यः ।।
Lord Brahma resides at the root, Lord Vishnu in the middle. The lord of all unborn Pasupati in the form of Rudra resides at the top.
Thus as Godesses Saraswati herself state "Sarva Linge Pratisthitam" ie. "Everything is situated in Linga". So, worship of Linga is highly auspicious and hence Linga form is worshipped.
2) Why is Shiva primarily worshipped in Linga form ?
Now, here comes this question. Other Gods and Godesses are worshipped in idol form whereas why Shiva is worshipped primarily in Linga form?
It is related with the inseparable relation of Shiva and Shakti and linga form represents it. The relationship of Uma and Maheswara is like that of word and meaning. It is illustrated in Vayaviya samhita Shiva Purana, Shiva-Shakti Vibhuti chapter:
शब्दजालमशेषं तु धत्ते सर्वस्य वल्लभा ।
अर्थस्वरुपमखिलं धत्ते मुग्धेन्दुशेखरः ।।
The beloved of Shiva (Uma) is in the form of words. The moon crested Lord (Maheswara) is in the form of meaning of those words.
So, just as meaning is formless and it gets manifested through words. In the similar way formless Shiva gets manifested through Shakti. The same chapter also states:
एवं परस्परापेक्षा शक्तिशक्तिमतोः स्थिता ।
न शिवेन विना शक्तिर्न शक्त्या च विना शिवः ।।
There is mutual dependence between Shakti and Shaktiman. There is no Shakti without Shiva and no Shiva without Shakti.
The inseparable relationship of Shiva and Shakti is also shown by image or idol form of ArdhaNarishwara form. However Linga form is the only form which establishes word-meaning relationship. It is because formless Shiva gets manifested in Linga form through the base of Shakti. It is shown in Linga Purana [part 2 chapter 47]:
विशोध्य स्थापत्येद्भक्त्या सवेदिकमनुत्तमम् ।
लिंगवेदी उमा देवी लिंगं साक्षान् महेश्वर ।।
The Devotee shall clean Linga along with the pedestal and then devoutly install it. The pedestal of the Linga is Godess Uma and the Linga is Maheswara himself.
Thus as pedestal of Linga is Uma/ Shakti herself, thus it establishes inseparable Shiva-Shakti relationship. It shows that Nirguna Shiva gets manifested as the base of Shakti. So as it represents the Nirguna aspect, Shiva Purana [Videysavara samhita chapter 5] states:
निष्कलत्त्वान्निराकारं लिंगं तस्य समागतम् ।।
He is also Sakala as he has an embodied form. He is both Sakala and Niskala (formless/Nirguna). It is in his Niskala aspect that the Linga is appropriate as it represents formless aspect.
And it also denotes the infiniteness of Linga as stated by Vyasa in Drona Parva [Chapter 202] of Mahabharata:
दहत्यूर्ध्वं स्थितो यच्म प्राणेत्पतिस्थितश्चयत् ।
स्थितलिङ्गस्य पन्नित्यं तस्मात्स्थाणुरिति स्मृतः ।।
Since he is great and ancient and is the source of the life and it's continuence and since his Linga form is everlasting, he is for that reason called Sthanu.
So, Lord Shiva is primarily worshipped in Linga form because it is the only form which establishes inseparable relationship of Shiva-Shakti, it represents manifestation of Nirguna in Saguna form and Linga is identical with the Universe itself and it represents infinity too. Thus it is best to worship Lord Shiva in Linga form.
Here are also answers which state Lord Shiva is primarily worshipped in Linga form due to curse of Sage Bhrigu. It is wrong because Lord Shiva is worshipped in Linga form from time beginning.
Curse of Bhrigu took place in recent Kaliyuga while Lord Shiva is worshipped in Linga form much much before that.
For eg. Rama worshipped Lord Shiva in Linga form. It is stated in Padma Purana [Patala Khanda chapter 104] and Lord Rama himself states it as:
विभिषणः कथमसौबद्धः श्रृंखलयानृभि: ।
Oh, how is it that Vibhisana seeing the Linga of Shiva, (called) Ramesvara and installed by me, is bound with chains.
And most importantly, curse of Bhrigu took place in this Kaliyuga, whereas there is a Mahapurana named Linga Purana which is among 18 Mahapuranas which is fully related with worship, origin, importance of Lingas and it is not that Vyasa wrote this Purana after curse by Bhrigu.
So, it is not due to curse of Bhrigu. Lord Shiva is always worshipped primarily in Linga form from time beginning.
The establishment of 12 Jyotirlinga:
Somanath Jyotirlinga, Mallikarjuna Jyotirlinga, Mahakala Jyotirlinga, Omkareshwara Jyotirlinga, Kedareshwara Jyotirlinga, Bhimashankara Jyotirlinga, Visveswara Jyotirlinga, Trayambakeshwara Jyotirlinga, Vaidyanath Jyotirlinga, Nageswara Jyotirlinga, Rameshwara Jyotirlinga, Ghusmeshwara Jyotirlinga
All Jyotirlingas were established in Linga form from the time of their establishment. They took much and much before curse of Bhrigu. Some took place even before birth of Parvati. For eg. Moon God established Somanath Linga during the time of Daksha Prajapati when he curses Moon God. Similarly Vaidyanath Jyotirlinga is related during the period of Ravana. And similarly all Jyotirlinga were established already before curse of Bhrigu.
Moreover Skanda Purana describes more than 108 Shiva lingas which were already established before curse of Bhrigu. Shiva Purana also states about Lingas like:
Rudresvara linga, Bhuteshwara linga, Bhimeshwara linga, Guptesvara linga, Vatukeswara linga, Kumareswara linga, Kameswara linga, Nadiswara linga, etc.. etc... so much
And these all were established in Linga form the beginning ie. Lord Shiva manifested himself as Linga form in those places. It is not that someone changed the image/idol from there and established Linga after curse of Bhrigu.
Thus it clearly shows that Lord Shiva was worshipped in Linga form from time beginning and it is not due to curse of Bhrigu.
Mahabharat also clearly states Lord Shiva to be worshipped in Linga form (and it is also before curse of Bhrigu). Lord Krishna in Anushasana Parva Dana Dharma section and Vyasa in Drona Parva[chapter 202] state the same thing:
ऋषयश्चैव देवाश्च गन्धर्वात्सरसस्तथा ।
लिङ्गमस्यार्चयन्ति स्म तच्मात्यूर्ध्वं समास्थितम् ।।
The Rishis, the Gods, the Gandharvas and Apsaras, always worship the Linga form which is supposed to stand upright.
Thus from the above facts it is ridiculous to say that Linga worship started after curse of Bhrigu. Curse of Bhrigu may have created only some coincidental circumstances. That's it only. Lord Shiva is worshipped in Linga form from time beginning.
Worshipping of Linga is highly auspicious as it contains all Gods and Goddesses, as it is identical with the Universe itself, as it represents the Nirguna Brahman, as it represents inseparable relation of Shiva-Shakti.
Lord Krishna in Anushashana Parva Dana Dharma section and Vyasa in Drona Parva [Chapter 202] states;
पूजयेद्विग्रहं यस्तु लिङ्ग वापि समर्चयेत् ।
लिङ्ग पूजयिता नित्यं महतीं श्रियमश्रुत ।।
He who adoreth Linga form of that high souled God, always obtained prosperity by that act.
And worship of Shiva Linga is in accordance with the Shruti/ Vedas. Taittariya Aranyaka of YajurVeda in 10.16.2 states:
भवाय नमः । भवलिङ्गाय नमः ।।
शर्वाय नमः । शर्वलिङ्गाय नमः ।।
शिवाय नमः । शिवलिङ्गाय नमः ।।
ज्वलाय नमः । ज्वललिङ्गाय नमः ।।
Salutation to Bhava and Salutations to Linga of Bhava. Salutations to Sarva and Salutations to Linga of Sarva. Salutations to Shiva and Salutations to Linga of Shiva. Salutations to your form of fire and Salutations to the Linga of fire.