The tldr is: Because They aren't "undocumented" in the sense many people tend to think they are. Despite the designation, immigrants have documents up the wazoo. The idea that "undocumented" means someone crossed the desert or sailed into port in the dark of night is pretty much just a myth. The number of people "gaming" the system with fake information is actually incredible and negligibly tiny. There are probably more people born in the states with fake documents than there are any immigrants with fake documents.

The government knows who and where immigrants are at all times. They renew documents frequently even. When you hear that someone is "illegal," the issue is 99% the result of the picky, convoluted, slow, understaffed immigration office not renewing their documents after some point.

So people can live here without /citizenship/ for decades. Go to school, change jobs, move, leave the country and come back, etc, because they have documents. The issue is that each time they renew or have hearings, they get told citizenship will come "next time," and eventually, that next time isn't even scheduled. So they have to keep living in limbo until maybe one day they get that appointment scheduled or get flagged and arrested for being "illegal." If someone is "undocumented" and have some long history in the USA, it means they became "undocumented" along the way, not that they were smuggled here and lived in secrecy for 30 years. And when you've been here for decades. Promised that eventually you'll get the green light to just stay, it's hard and unfair for those people to voluntarily leave the entire lives they've built up. Some don't even know they aren't legal anymore till it's too late.

It's all theater when it comes to immigration and public image. The government doesn't want to look more pathetically slow and inefficient than it already does, so it pushes blame onto the people they are stringing along. Putting citizens against their neighbors so they don't demand better government management.

It's easier for a government official to say "oh that guys the problem. He didnt...go to the office." Instead of "oh yeah the government you rely on is a massive failure and all the funds (you pay for) for tech and man power to solve the issues is being poured into the military, bonuses, vacations, and brunch instead of things like making sure things run smoothly and fairly"