Except you can't natively select text for copy/paste anymore.
When you click-drag you're now triggering a tmux selection, not the native terminal-emulator highlight. This is a big problem because the emulated variant is slow and behaves nothing like the real thing.
To my understanding this is also a problem that can't be solved without further terminal emulator support. As it stands the remote application (tmux) can either receive all mouse-events or none of them.
This means you have to choose between scroll-wheel support plus broken text-selection - or no scroll-wheel support.
I tried the mouse integration and turned it back off for the same reason as you. Not having copy-paste at the terminal level is a non-starter as far as I'm concerned. Learning the vim movement commands better eliminated most needs for the mouse-pointing ability anyway.