Why do ISKCON saints only preach about God Krishna and say that we should only worship him and no one else?
That is so because ISKCON stands for International Society for Krishna Consciousness.
It is their personal recommendation, nothing else.
Because only Lord Krishna has displayed vishvaroopam (universal form) so far. No other god or goddess has done that so far. This is also confirmed in the Vedas specifically Atharva Veda.
In the Atharva-veda it is said,
yo brahmāṇaṁ vidadhāti: pūrvaṁ yo vai vedāṁś ca gāpayati sma kṛṣṇaḥ.
यो ब्रह्माणं विदधाति: पूर्वं यो व्ऐ वेदांश् च गापयति स्म कृष्णः.
It was Kṛṣṇa who in the beginning instructed Brahmā in Vedic knowledge and who disseminated Vedic knowledge in the past.
Then again it is said,
atha puruṣo ha vai nārāyaṇo kāmayata prajāḥ sṛjeya ity upakramya.
अथ पुरुषो ह व्ऐ नारायणो कामयत प्रजाः सृजेय इत्य् उपक्रम्य.
Then the Supreme Personality Nārāyaṇa desired to create living entities.
Therefore Lord Krishna is God almighty.
Because they are an off-shoot of Gaudiya Vaishnavism and Gaudiyas believe Krishna is the supreme God. The basis may be the Brahma Vaivarta purana about which wiki says
"The text is notable for identifying Krishna as the supreme Reality and asserting that all gods such as Vishnu, Shiva, Brahma, Ganesha are same, and all are incarnations of Krishna."
They also claim a scripture called "brahma samhita" was discovered by Chaitanya that asserts Krishna is the supreme God.
1.Why do ISKCON authorities only preach about God Krishna?
Because it comes from a Gaudiya Vaishnava Lineage that consider Sri Krishna as the Supreme God.
2. Why do ISKCON say that we should only worship him and no one else?
Because they are of an opinion that as Sri Krishna is the highest God, to worship him, one should not worship other forms of God.
I am mentioning Sri Krishna's and Mahaprabhu's views here as thses are relevant for anyone following a Gaudiya Vaishnava sect.
Mahapprabhu ordered His Vaishnava-devotees to worship every form of God and ask from them their grace so that the devotee can have single-minded devotion to Sri Krishna.
(According to the Gaudiya Vaishnava Mahajanas, **Mahaprabhu appeared on earth to preach the aspect of sweetness (maadhurya-bhava) of God in place of the greatness (Aisharya-bhava) of God.
"prabhu kahe: Maadhurya bhagavatta-saar" meaning sweetness is the essence of the Divinity.
Sweetness is best expressed in the Gopijanapriya Krishna form, Who is ever beautiful, charming and not holding any weapon. The santa,dasya, sakhya, batsalya and madhura--hese five bhavas are the most beauiful relations one can have with Sri Krishna. So having single-minded devotion to Sri Krishna is the most sweet and beautiful form of the Sanatana Dharma.Reference: Gaudiyamate Brahma-Tattva in Gaudiya Vaishnava Darshan,Principal Radhagovinda Nath,D.Lit.,page 119-139)
By the way it is not that Sri Krishna alone showed Visvarupa. Lord Shiava showed Visva-rupa to Sri Rama (as mentioned in Shiva-Gita) and Devi showed Visvarupa to King Daksha (as mentioned in Bhagavati-Gita).Mahaprabhu never focussed on the Aiswarya-bhava of Visvarupa as I mentioned earlier.)
As per Mahaprabhu's teachings, to attain this single-minded devotion to Sri Krishna, one has to be a pure soul and so devoid of any bigotry or hatred towards anyone, be it a form of God or a human or non-human being. This has been repeatedly said by Sri Krishna also in Srimad-Bhagavatam and Gita.
Reference: Mahaprabhu Sri Chaitanya,Radhagovinda Nath, Sadhana Prakashani.
It is based on Chaitanya Vaishnavism. They have their Vedanta system as per which Krishna is the supreme, source of other avatars. He is said to give special rasa. They worship Chaitanya also, who is Krishna according to them.
And devata worship is not prohibited, though they don't have any deities of other devatas in their temples. And they worship Narasimha daily and in some temples they have murtis of Rama as well. AFAIK on yatras, they go to other devas(i mean other than vishu related like siva, ganesa, durga etc.) temples also to pray for bhakti like Chaitanya did on his south indian tour.