It's very annoying to "keep guard" of bugzilla when people reopen random bugs for no good reason. Ever since this has been allowed, I've estimatedly had to reclose 2-3 per day. Please restore the old functionality.
Reporters can reopen their own bugs. Other users without editbugs privs cannot. This is not a new behavior. It has always been so.
I don't think it is a good idea, many other bugs would get lost because the assignee or somebody else doesn't always notice new comments in such cases :D But if you mean that people reopen bugs of *other* people then its a bug that should be fixed.