screen reimplements its own internal permissions model
That's exactly my point. This is neither categorically good nor bad. It doesn't reinvent permissions gratuitously, but, rather, as a way of increasing flexibility.
It allows per-window permissions and fairly arbitrary permissionsetting, for any user, without resorting to groups (the membership of which a regular user does not control) or universal permissions.
setuid I could handle if it were just that, but screen reimplements its own internal permissions model, while tmux simply uses unix permissions, which everyone already understands. Composability wins.