It moves the discussion further to the right and legitimizes Republican talking points for the majority of people who will only hear a brief soundbite about this, rather than diving deep into the matter.
Besides, the GOP isn’t about to run out of bogeymen to trot out just because they could get what they want on the border. They can take it as a compromise and try to push things further down the line. Or they can decide this is good enough for now, and start railing against something else. Union membership rising being a Chinese plot to infiltrate the US and install a Communist dictatorship, so we better write some new laws to enable even more union busting. Free school lunches for kids from poor families turning them gay AND communist by getting them hooked on the government teat early. Woke public libraries turning kids trans by letting them check out books that don’t universally demonize it, so better put some sort of draconian funding limits on them. They’ll find something else, don’t worry.
The way you’re framing it and Congressional Democrats approach these things only work if the Republicans aren’t completely shameless, above doing things that should completely destroy any remaining vestiges for their voters, but this has been disproven time and time again by the actions of the GOP. If they think they’ll have half a chance, they’ll wring out even more concessions on this front from the Democrats by pretending to offer something they immediately renege on, just to leave the Democrats going “Aw, shucks, fooled me again. I thought you said you weren’t going to do this again.”
I mean, the Democrats didn’t really leave these people to rot, they’ve largely been prevented from doing anything to help them since rural areas vote so overwhelmingly Republican. What do you really expect the Democrats to have done when it’s the other party these folks keep electing to represent them? They effectively say they want the policies that have left them so exposed and disadvantage, then they have a shocked Pikachu face that “those darn liberals haven’t done anything to help us.” Heck, even in broad terms, their voting habits have screwed all of us by preventing broadly popular things like universal health care or drug reform from going forward because of the disproportionate power the self-destructive votes they cast wield at the national level. My sympathy for them is extremely limited, and my patience at their insistence in making everyone else suffer for their god-awful politics has long since run out.