My solution is this: secure the border for real, stop government hand outs and benefits to non citizens, deport felons as arrested. If we did that, and just that, this situation would unravel itself in 2-3-4 years to a large degree. It would not be perfect, but there would be a vast improvement.
This situation evolved over 60 years of a porous border. There is absolutely nothing that will make it go away quickly. There just isn’t.
That said, what you are advocating is attrition thru enforcement. I agree with that. No legalization period and enforce our laws. We should also make e-verify mandatory--not voluntary as it is now and then really crack down on employers who knowingly hire illegals. Shut off the job magnet.