It's not quite that easy. In order to get a visa, people need to have identification in the issuing country. This means they have names, addresses, relatives, etc. This makes them much easier to track down here. Once the flood of illegal border crossing slows to a trickle, and the visa overstays are attacked with vigor, that too will slow.
I pray you are right! MAGA!!!
We now have machine readable visas. We know who comes and goes because they are put into the data base when they arrive. Since we know how long the visa is good for, anyone who doesn't show on the exit data base is a visa overstay,
Note that there are 38 countries in the Visa Wavier Program and don't require visas. They can stay up to 90 days without a visa for business or tourist reasons. They must still fill out an arrival and departure form.