> because tmux inside tmux is very inconvenient.

Hitting c-b c-b isn't that inconvenient?

Agreed.

I hold Control and double-tap b for managing the remote session, then everything else is the same.

Granted, I'm not a power user, so there may be numbers that get frustrating. I could imagine complex splits getting confusing (I don't use splits at all).

C-b is less ergonomic than C-a that is the default on GNU screen. The first thing in tmux is to remap to C-a. (Triply so if you remap caps lock to ctrl.)