Comment by bonsai_spool

> Not just that, universities (especially smaller research universities) love having grad students whose research is paid for.

> Why would the university not pick that over a local kid who the university has to pay for out of their own coffers?

Universities don't pay for research - and departments usually don't pay for research either.

At the margin, a professor will prefer someone who has her own funding, but that person also needs to be competent, so I doubt the national schemes you are citing have made an impact on who gets into graduate school.