Reason Why Shiva dosn't worship anybody whereas Vishnu worship Him in all His incarnation
In Hindu mythology, Brahma, Vishnu and Shiva, the holy trinity are known as the creator of the Universe — however, while Vishnu worships Shiva in all his incarnations, Shiva, known as the destroyer does not worship anyone. The reason behind this is :
While, according to the Bhagwata Purana, Vishnu is more supreme than Shiva, however, according to the Shiva Purana, Vishnu and Brahma were created from Aadi Anant Jyotir Stambha of Shiva, hence making Shiva more powerful than the two. This could, thus, be the reason that Shiva does not worship anyone.
Another reason could also be that Shiva is the only Supreme Paramatma as he is unborn (Ajanma), Akarta and Abhokta (Vairagi) as said in Geeta that God is Ajanma, Akarta and Abhokta.
God is neerakar (shapeless and formless), Shiva Linga is the symbol of Shiva’s nirakar form only.
And also Vishnu always advised other deities (Kartikeya, Indra, Parvati, etc.) to worship Shiva only if they have mistakenly committed sins.
Now, Lord Rama, an incarnation of Lord Vishnu established Shiva Linga when he was marching towards Lanka which is known as Rameshwara Mahadeva meaning Ishwar (God) of Rama. In Ramayana, when Lord Rama wanted to do Prashchatap because he considered killing Ravana as sin of killing a brahmana, he asked Hanumanji to organize to establish a Shiva Linga and asked again Shiva for mercy and to cut his sin.
In Krishna avatar of Vishnu, when Krishna wanted to bring some tree Kalpa Vriksha from Indra, he worshiped Shiva for blessings and that is known as Gopeshwara Mahadeva in vrindavana meaning Ishwara (God) of Gopal (Krishna). Also when Krishna wanted to have a son, he asked sages and from their advice he prayed to Lord Shiva to get a son. He said during “Shive Sarvadhi Sadhike” meaning nothing happens without Shiva’s will during the prayer in expectation of being blessed with a son!! When the Mahabharata was about to be battled he asked Pandavas to have bliss of Shiva first and arranged a Pooja of Shiva Linga.
In Bhagwata Purana also, there is a story about Lakshmi Devi’s unhappiness with Vishnu because Vishnu told her that half area of his heart is dedicated to Lord Shiva only. And in the rest of the half, all the creatures of world and all deities including her wife Lakshmi lives!
Thus, we can see that Vishnu has taken Rajas nature and Shiva has taken Sattva. Rajas is full of desires and action and hence He worships Shiva to fulfill the desires, this way He shows how to worship the God whereas Shiva is satvik, He is self realized and self sufficient and hence He doesn’t appear to worship anyone externally.