Honestly the system could be fixed by doing any one of the following:

1. Putting in place a statute of limitations. The government doesn't successfully remove you in 10 years, you get permanent residency.
2. Reinstating 245(i), fine, you broke the law, find a sponsor, wait through any appropriate backlog, pay a fine, file for AOS.
3. Getting rid of re-entry bans, similarly to 245(i), fine, you broke the law, find a sponsor, wait through the appropriate backlog, leave, go grab your immigrant visa, and return.

What we're seeing right now is a direct consequence of IIRIRA where they got rid of old version of 245(i) and placed re-entry bars, and the illegal immigrant population ballooned because the safety valves were removed. Lets face it, people will always overstay, stowaway or get smuggled on a ship or a plane, or hop across a shitty TrumpCo. fence. Just before IIRIRA you could eventually get right with the law one way or another, right now what option(s) do you have? Marry a USC, become a parent to a USC and try COR or wait 21 years, go get shot in the hood to get a U-visa, or try a hail Mary with asylum since you better have a good reason you didn't file within 1 year as mandated by the RealID Act.