I've heard the argument before, and I can understand it. But I reject it categorically, based on real-world evidence. Either Europe and Canada disprove the assertion that capping payments restricts innovation and reduces service, or the US is subsidizing innovation and service for the rest of the world. In either case, it's not so simple as "capping prices punishes the providers," and I'm not OK with the situation the way it is.
Here's another way to think about it: we don't know what a regulated, price-capped, or even universal healthcare policy would do in the US. People have been making your argument for a very long time in US politics (since the 70s, at least, when the employer-subsidized insurance market started to show "issues"), and it's been used as political cover to keep (or patch) the system while maintaining incredible profits for pharmaceutical companies, insurance providers, specialist MDs, and large medical service provider conglomerates. Meanwhile, elsewhere standards of care, service, and innovation are comparable (or better) than in the US, and prices are much, much lower. What's missing? The incredible profit margins accruing in the US.
So, rationally speaking, I'd like to try instituting reforms that have worked elsewhere. What all of us agree on is that the current system only works for the wealthy and healthy. The AHCA literally just rolls back regulations to pre-ACA days and simultaneously undercuts Medicaid (see the released version from the Senate today). It's not a "fix," it's going back to the "bad old days."
I'd like to try a fix of the system for once. Price caps, single-payer, or anything else that some bright person can come up with that is also based on real-world evidence rather than pie-in-the-sky thinking or partisan ideology.