Why is it not ideal to rely on interactive assumption to build PRF? I understood the meaning of interactive assumption from
What is the notion of an interactive assumption?
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However, I am not sure why there exists a research field of constructing PRF 
 from standard assumption.

What is the advantage of standard assumption over interactive model in general and especially for PRF?
The advantage of a non-interactive assumption is that you prove something in general . In contrast in an interactive assumption you prove a specific instantiation of the problem. Think a variety of DL problems like DDH. The game starts with the challenger choosing the challenge. The challenge is given to the adversary and then the later is trying to solve it. That means for any instance of the problem. In contrast in an interactive assumption there is a learning phase like in CPA proof whereby the adversary is learning: is asking queries to the encryption oracle. That being said the proof is specific for that interaction. In some sense it is weaker because you cannot predict if there is a craft query that will break the system.