I use to have a few terms active in the very early days of Linux. When I heard about screen/tmux now I just have 1 term open and multiple tmux sessions.
I think if you can get use to tmux/screen you may like that better :)
I find A good window manager to be nicer for a bunch of terminals than tmux, where tmux really shines is when you want a bunch of terminals on a remote system.
I've faced the many terminal tabs issue. In a way tmux actually makes it worse as I'm used to the running app being in the title, and tmux obscures that (now there's just "client"). But also better as I found a great session restore plugin; always drove me a bit crazy when something happened that either killed the terminal app or triggered a full restart, and my tabs were lost.
I think if you can get use to tmux/screen you may like that better :)