To be honest, I have never played on sites that do not require verification. I play at casinos in poker rooms. It is more convenient for me that way, as I can control my bankroll. I would also be unlikely to trust my money to websites that do not require verification.
Verification is a problem, for example on 888. I went through it for about a month. If you have old-style documents, such as an internal passport of a Ukrainian citizen, it can be quite a complicated procedure. On the other hand, verification prevents fraud to a certain extent, which makes the site more secure. I think there are more advantages.