Why didn't Shankara eliminate the idol worship?
How could he? He was not just any scholar biased by his own views and prejudiced to others, he was a true knower of the Vedas and scriptures. From answers like this you can know that scriptures support both sakara(with-form) and nirakara (formless) Brahman. Adi Sankarachrya only preached one aspect of the whole truth as it was required for that time to win over the Buddhists.
During his time Buddhism was spreading widely in India. So by his scholarly work he created a doctrine that was easier for Buddhists to accept. The Advaita philosophy was pseudo-Buddhist in nature and hence it was a compromise that was easier for the Buddhists to accept. So by preaching the Advaita philosophy Shankaracharya blocked the widespread of Buddhism and by establishing various temples, chardham, etc. at the same time he revived Hinduism.
So at one hand he defeated Buddhist philosophers through his advaita philosophy converting them to Hinduism and at the other hand he promoted idol worship and established various dhams, monasteries etc. to strengthen Hinduism. So reviving Hinduism was the purpose why he also promoted idol worship.
From the scriptures it is known that Shankaracharya was actually an incarnation of Shiva and he had taken birth for that purpose only. Chapter 30 of Kurma Purana says
तदेव साधयेन्नृणां देवतानां च दैवतम्।
श्रीतस्मार्तप्रतिष्ठार्थ भक्तानां हितकाम्यया।
उपदेक्ष्यंति तज्ज्ञानं शिष्याणां ब्रह्मसंज्ञितम्॥ ३४॥
सर्ववेदान्तसारं हि धर्मान्वेदनिदर्शितान्।
स्वधर्मा ये निदर्शिताः।। ३५।।
The people should adore lord Mahadeva, who happens to be the god of
gods. The brown complexioned Siva, for the establishment of Srauta
(Vedic) and Smarta dharmas (belonging to the Smritis), and for the
welfare of the devotees shall incarnate on earth. He Will enlighten
his devotees on the subjects of the gist of Vedantas, the knowledge
relating to the Brahman, and all the dharmas enshrined in the Vedas,
which have been narrated earlier.
Hence, even though he preached the theory of impersonal Brahman, he himself was a great devotee of Lord Krishna. This is evident from his numerous writings like Bhajagovindam, Achyutashtakam, Jagannathaastkam, etc. In Prabodh Sudhakar he writes:
bhuteṣvantaryāmī jñānamayaḥ sadcīdānandaḥ
prakruteḥ paraḥ parātmā yadukulatilakaḥ sa evāyam 
The crown jewel of Yadu dynasty, Shri Krishna, is the all knowing supreme soul of the form of knowledge and eternal bliss who is beyond prakruti (material nature/maya) and resides in every being.
So his philosophy was for a special purpose, but internally he was a devotee. His devotion for Vishnu or Krishna is only but obvious because Shiva is the greatest of all Vaishnavas [SB - 12.13.16]. Hence, even though he preached theory of impersonal Brahman, didn't eliminate idol worship.