It seems to me that there is a dichotomy between that or allowing companies to continue to snub US workers for vulnerable foreign labor.

Maybe you could escape the dichotomy by requiring H1-B workers to be in the 5% paid employees at a company or something.

No, what needs to happen is to give workers mobility. H1B workers are preferentially hired at some firms because of their lack of mobility — they're easier to abuse than other workers. Addressing that would let everyone be on an equal footing and share the benefits of agglomeration (immigration increases supply and demand!) It would also be far more just and equitable.

Parents idea is better.

I think from a US citizen perspective, you don’t want to be equitable with people on a Visa program, because the low COL areas where many of the people on H1-B visas come from inherently makes them more willing to accept less than their US counterparts.