The way this is currently handled is that when an author identifies that their article is funded by the NIH, the Howard Hughes Medical Institute or some others,

The way this is currently handled is that when an author identifies that their article is funded by the NIH, the Howard Hughes Medical Institute or some others, it is automatically flagged to become public access in a year. Several of my own articles that were behind paywalls are now open access under said system. Free access and copyright transfer aren't necessarily in opposition.