>>We need a system to track and deport visa overstays.<<
I would lay 10 to one odds that the system of tracking you want is already in place, and I say that without any particular knowledge of the system.
What we need is a President who will permit the tracking to actually take place, and who will also permit the border enforcers to take action upon the information. That is what has been lacking. Obama has been the worst, but Bush wasn’t much better in that regard.
The US-VISIT system was authorized but never implemented in 1996. We really do lose track of people when we try to process entry visas versus exit visas. There are also about 30 countries under the visa wavier program. And we have issued around 4 million border crossing cards (BCC) to Mexicans who can come and go as they please within a certain limitation on how far inside the US they can travel.
Internal enforcement has been virtually stopped under Obama and Bush 43 was the worst until Obama came along. There is also very little cooperation by colleges with ICE. At any one time there are over 900,000 foreign students attending US colleges. Many of these students just disappear.