Muon2 and I, I think, have decided that "independent" commissions need a lot of constraints to work well. Otherwise, the commissions tend to be gamed, and those claiming to be "independent" tend to fall considerably short of that. Those without reasonably tight parameters have tended to go off the rails. I don't think either of us have been particularly impressed.
Even the best gamed independent commissions (say Arizona) will come up with results similar to the better kind of legislative-map-by-one-party-with-serious-constraints (the new Florida map, say) - and clearly better than the worse examples of that (say Michigan).