Running m0’s has illustrated to me that the timer sometimes causes people to be cranky when, absent the added pressure, they can still have fun/good attitude when something goes sideways.
I suggest that D3 style greater rifts system for selecting you m+ difficulty would be perfect.
-You can enter a dungeon at any keystone level that you have unlocked. You unlock the difficulty by successfully timing a lower difficulty (+1, +2 etc).
-You can choose lower difficulties than your max available if you want
-You can take a run at your highest available difficultly if you want (with reduced rewards if you don’t time it - but your key doesn’t deplete and you don’t lose the opportunity to attempt the difficulty again)
I don’t think it would be significantly different than the current system, but I do think could solve a lot of anxiety and just generally feel more fun.