While all MUA sucks UI/UX for most web forums even worse - much higher response time, and a lot of mouse clicks for navigation (instead of familiar keyboard shortcuts). Some sites do support shortcuts but they differ from site to site while with MUA you need to learn them only once for all maillists.

I agree that requirement to subscribe to a maillist is an entry barrier which doesn't exists for web forums but once you're are subscribed it is faster to skim messages in a mailbox.