There has to be a compromise on immigration. Perhaps people illegally staying here won't be eligible for citizenship and have to pay fines/do community service. Some punishment for breaking the law is necessary as a deterrent. That said, we should massively increase legal immigration and we need them to fill open jobs to help get inflation down in areas where we are losing workforce.
As long as the issue of immigration can be used to get GOP and Dems elected, neither side will do something about it. Remember both parties had control of the government at various times yet kept blaming the other party for their viewpoint.
The southern border is swiss cheese but the majority of people here that are undocumented/illegally are simply visa or legal crossing overstays. There is no system to track people who fly in or legally cross and simply never leave. Rather than spending billions on a wall which cannot cover the entire border due to geography and the fact that ladders were invented, spend less than half of that on an entry system to track people better with a data base. ICE has no time or manpower to do this as it is now but that is an easy fix over a few years to cut illegal population in half.
As for the southern border itself, the natural border makes it impossible to simply erect any barrier nor can any such impediments stop the drive of thousands who are desparate to cross. The U.S. system has always rewarded people who can physically get to U.S. soil in one way or another. A family who left El Salvador and crossed a few countries to get to the southern U.S. border is not going to simply stop there. People hate to hear the truth but there is nothing to stop people from making the trip. The question is what to do when they show up. There is no solution to this problem as long as parts of Central America is haven for corrupt governments and poverty. There is a reason why there are no Panamanians or Costa Ricans making the trip.
GOP wants to win on closing the border but you cannot physically close a border like U.S./Mexico and even GOP does not want to round up people in buses and send them back over...bad optics. Dems want to tug at your heart strings about how open U.S. is but then coudl care less about those people once they cross that border. It is all about optics and tapping into the voter sentiment only.
There are some issues where there are no solutions, only fingers in the dykes to slow down the water.