Do you think all higher education should be completely free, like it is in many countries?
Only in STEM subjects though. I think it was America where someone was talking about how 50,000 people graduate in Law each year when there's only 30,000 jobs as lawyers in total, it's a ridiculous situation. Youtuber Vee said it's the same thing in Romania, he got a degree in Law, but now he's having to retrain as a doctor to find a job.
If they're based on academic merit, then I think those could work to incentivize students, so sure. What's most important for the US right now though is addressing why university is so astronomically high in the US.
What about national scholarships based on academic excellence (as opposed to skin color and gender)?
Nope, definitely not! And it's not free anywhere, it's simply paid for by taxpayers instead of individual students. The US needs to reform its higher education system, but paying for it through taxes is not the way to do that.