It sure would be good but on the other hand there are also countless normal or even interesting questions asked by anonymous simply because some people seem to feel the need to always be anonymous for some reason, so by blocking the entire anonymous section of gag you might miss out on those questions as well. I see your point but for me personally, I don't think I'd use that feature as I would still be curious for the interesting questions asked by anonymous & I would just keep trying to ignore the idiotic ones.
If you don't like the question and feel like it will only bring "pointless arguments" then don't answer it, I don't see why anonymous questions as a whole should be blocked in general just because a few people don't like heated discussions.
When I go anon, it's because I don't want to get PM'd. If someone, anon or not, starts trying to argue over something silly, I stop replying. I agree with you, I dislike pointless idiotic conversations. :/ I went ahead and voted for I just avoid them.
It's probably a better idea to simply activate self-control and practice self-discipline rather than asking GAG to invent a feature so you don't have to. If you block all of the anonymous questions, then you will also inevitably block those people who are using the anonymous feature to be transparent and vulnerable in a way that gives you insight you would have never had if it weren't' for the anony feature. Yes, some people abuse the anonymous feature, use it with the wrong intention, or fail to take advantage of what it can do but not everyone does.