I don't think the problem is with the foreign people accepting lower wages and forcing more competition. I believe it is more of a symptom/mechanism of wage theft. Which has been going on for decades to bleed the workforce dry and enslave them through unrepayable debts.

Though I believe foreign graduates taking less pay for employment is not the problem or inherently bad, it's not helping workers as a whole.

I believe that in addition to your suggestions there would need to be stronger wage and worker protection laws to prevent companies from clearing out employees with longer tenure/higher rates of pay before enacting this specific type of policy.

I think that would allow for a more healthy competition where incumbent workers/natural citizens won't be replaced/undercut by foreign graduates who have to debase themselves by taking lesser pay for the same work.

In my opinion it's as if Trump would do this as a way to weaponize cheaper labor against the working class so corporations can improve their margin by slashing labor costs.

I could be totally wrong, and am open to other opinions but maybe that's where OP's line of thinking may be.