It's not like someone would forbid Warren Buffet from doing so. The government already set up a system that is all but in name compulsory. So, let's take a pile of the same size as the current system uses, but let it go through a single arbiter, with combined purchase power.
We have a system like that for student loans—where the federal government itself originates and owns 90% of student debt—and it has led to massive cost inflation. What makes you think we’d implement a healthcare system better?
The federal government hasn't even lifted a finger to control undergrad education costs. In British Columbia, Canada where I'm from, the government sets limits on student loan coverage (seems to be CA$520/week right now) and universities don't get anything more from student loans. When my student loan disbursement occured, the form explicitly had $5000 of "unmet need" that I would need to scrounge up somehow.
If a universal healthcare system really wanted to, it could keep costs under control in a similar manner by telling hospitals to accept X amount for Y procedure or get bent. That the government doesn't swing its big dick on colleges in the US is entirely the fault of the government and a populace that always votes for "candy for dinner" vs. "eating vegetables".
