You'd think that college tuition would decrease in the US because university enrollment has actually been on a downward trend for over a decade. However, in the US university primarily serve as social signalling and an elite prestigious university is a very different type of product than a typical university (most of which are not particularly exclusive, admitting over 70% of applicants).

Presumably, competition prevents this. It would really depend on the applicants' other options. Between attending Vanderbilt at $200K per year and a moderately less prestigious state university for about an order of magnitude less a lot of students would pick the latter. The university could admit more students that are willing to pay the doubled tuition, but that'd probably result in lower graduate quality.

I'm not sure what could make elite universities lower their tuition save for legislation. As the Varsity Blues scandal demonstrated, families are willing to pay huge sums of money to get their kids into elite university. Besides laws, the only other answer I can think of is to reduce the prestige of elite universities. If an Ivy League, Stanford, or MIT diploma ceases to confer so much advantage in academia and the labor market then their ability to charge large sums would go down.