Nice to think about, but the set of circumstances that might lead to it are exceedingly narrow.

Most of the seven states that have independent commissions adopted them by a citizens’ initiative. Since Texas doesn’t have that option, the only way it would happen would be if lawmakers voluntarily gave up their redistricting power.
Kathay Feng, national redistricting director of the progressive government watchdog group Common Cause, said that’s unlikely to happen in Texas, but not impossible.
“The reality is that when a legislature is looking at potentially split control or the changeover of control from one party to another, they’re the most likely to entertain the possibility of redistricting reform,” Feng said.
Rice University political science professor Mark Jones said it would take a unique set of circumstances.
“It would take us reaching a tipping point where Republicans are pessimistic about their prospects for retaining a majority, but Democrats are also pessimistic about their prospects for taking a majority as well,” Jones said.
I think Jones’ assessment is basically accurate, but it’s important to understand what Republican pessimism about retaining a majority means. We’re talking about them being afraid that they might face unified Democratic government in 2031, the next time redistricting will come around. And not only must they fear this thing that might happen ten years and three statewide elections from now, they must conclude that their best option now would be to curb that future theoretical Democratic hegemony via the creation of an independent redistricting commission. All this happens following a Democratic takeover of the State House, because otherwise Republicans can do what they’ve done before, which is draw whatever districts they want without fear. You see what I mean by exceedingly narrow?
Let’s keep one other thing in mind here. If we do get a Democratic State House, Republicans can still push for whatever maps they want for the SBOE, the State Senate, and the State House. That’s because if the two chambers can’t agree on maps for those three entities, the job gets thrown to the Legislative Redistricting Board, which is the Lite Governor, the Speaker, the AG, the Comptroller, and the Land Commissioner. In other words, a Board on which Republicans would have a 4-1 majority, and thus no trouble passing those Republican maps. The one map that would still be up in the air would be the Congressional map. If there is no map passed legislatively, it gets thrown to a federal court, over which neither side would have any control.
There is room in this scenario for some compromise. Republicans would prefer not to let a court do this work. Democrats would of course like to have some influence in the mapmaking process. You can imagine an agreement to draw maps for all four entities – Congress, SBOE, Senate, House – that leans towards incumbent protection rather than greatly advantaging or disadvantaging one party over the other. If that happens, you could also imagine them including an independent commission as a bonus Grand Bargain, but that seems a bridge too far. But compromise maps that mostly don’t make any incumbents’ lives too difficult, that I can see maybe getting done.
Maybe. The situation I’ve just described here is like what happened in 2001, which was the last time Dems controlled the House. The LRB drew the state maps, which led to the massive GOP takeover in the 2002 election, and a court drew the Congressional map. And then, once Republicans had control of the House, they went back and redid the Congressional map. That was the original, stated motivation when Tom DeLay pushed for re-redistricting in 2003: The Congressional map should be drawn by the legislators, not by a court. Obviously, they wanted a map that was much more favorable to Republicans, but that was the original reason they gave. It seems to me that this is a very plausible outcome in 2021 as well – the Republicans decide to let a court draw the map, which in all likelihood would be quite deferential to incumbents anyway, then take their chances on retaking the House in 2022 and doing a new Congressional map again. Hey, it worked once before, and now they have a more favorable Supreme Court to back them up.
Honestly, this may be the single most likely scenario – the LRB draws the state maps, a court draws the Congressional map, and everything hinges on the 2022 election. Maybe Dems keep the State House. Maybe we manage to elect a Democratic Governor, who could then veto any new Congressional map. Maybe Republicans win and do their thing. Heck, even in the Great Map Compromise scenario, who’s to say that Republicans wouldn’t tear it all up and start over in the event they retake the House and retain the Governor’s Mansion? I’d put money on that before I placed a bet on a redistricting commission. 2031 is a long, long way away. It’s not at all irrational to prioritize the now over what maybe could possibly happen if everything goes wrong.