No? Prices are market-driven in our society, not necessarily a function of labor costs. In the very long-term best case scenario, the increased profits going to the company from these efficiency gains may encourage more competitors to pop up, and either drive prices down or offer more for what you pay.

I'm not sure who even is priced out of healthcare considering if you are broke you get covered and if you are a little less broke you get subsidized care and if you aren't broke, then you finally pay up. It isn't really rooted in free market dynamics like you'd expect with theoretically falling labor prices because of stuff like ACA or medicaid covering the people who would have been more price sensitive.

> theoretically

In case you haven't noticed, all that our current system is able to do with increased efficiency is cutting staff and/or increasing the percentage of money that gets siphoned up to capital holders.

Healthcare prices are not dictated by labor costs, but by how much the leeches who own everything are willing to charge people for it. For example, insulin is dirt cheap to make, yet billed at exorbitant amounts.