As your source notes, the US tends to do average on point of care metrics (e.g. hospital outcomes, versus other similarly developed countries), but worse on lifelong metrics that would conceivably be impacted by income disparity (e.g. life expectancy, maternal mortality).

The metrics the US does poorly on seem like they're more of an access problem (than acute care being bad), which suggests broadening access to affordable healthcare would be the best redress -- i.e. universal healthcare.

The US health system seems like it would be better served by explicitly breaking it into a multi-tier one.

Basic tier: universal health care for basic access and procedurings, including proactive health measures

Everything else: private health insurance available (not attached to an employer)