Yes, this sounds unreasonable right now because prices are so high. But bear with me for a second.
Most healthcare in the US is paid through insurance. Insurance creates moral hazard. Insured patients generally don't even need to know the prices of what they're buying, much less negotiate those prices. And here's a dirty secret: insurers don't care much either. They simply add a margin on top of their actuarially-forecasted cost. So healthcare prices rise dramatically over time, because relatively few people are directly exposed to them and push back on them. From this perspective, healthcare insurance is a problem, not a solution.
Don't get me wrong, there are admittedly some obstacles to patients paying out of pocket right now. My point is that we know properly functioning markets set fair prices, and we know our healthcare market is dysfunctional. Healthcare insurance plays a part in that dysfunction.
Patients negotiating directly for better prices eliminates moral hazard and restores market function. Strategically, that would finally restore pressure on healthcare providers, who have become accustomed to raising prices with very little push-back. Without some kind of push-back, providers will continue raising prices - because they can.