How do you keep those illegals from doing just that? A mass database?
First, I don't think you are aware of what the touchback scam entailed. Essentially, the illegals were supposed to go away for a weekend to their home country, go through processing stations, and return to the US. They were registering in the US prior to going back home and their US employers would be waiting for them to come back. So yes, there would be a database.
For those who would go back and actually get in line outside of any touchback scheme, it would be difficult to track them unless they appeared in a US database, e.g., prison/police records that could be checked upon applying for entry into the US as part of the security check.
As someone who has actually issued visas overseas to enter the US, most of the illegal aliens in the US wouldn't be eligible to receive a tourist visa let alone an immigrant visa. FYI: There are over 3 million intending immigrants overseas who have completed all of their paperwork and are awaiting their turn to enter the US under the various immigration categories. Can you imagine adding another 12 to 20 million to those numbers? We take in 1.2 million legal immigrants a year now.