As a US citizen with a PhD, I didn't experience any clear discrimination in favor of foreign students during grad school.

I think the main reason so few US citizens get PhDs is because PhD "student" (they're actually workers) positions pay so poorly. Make PhD student positions have non-poverty wages and you'll see a lot more interest from US citizens.

On the flip side, I think foreign students experienced a lot of abusive conditions that I could more easily say no to because I didn't have a visa that required me to work at the university. I've seen some of that first hand. I don't mean to imply that there would be no cost to me saying no, just that I wouldn't have to leave the country if I said no.