What really needs to be done is the government needs to require all research that is funded at all with tax payer money (which is the vast majority of research) must be open access to all
Here are links to the major US funding agency's policies.
NIH Public Access Policy: https://publicaccess.nih.gov/policy.htm
NSF: https://www.nsf.gov/news/special_reports/public_access/
DOE: https://www.energy.gov/sites/prod/files/2014/08/f18/DOE_Publ...
DoD: https://discover.dtic.mil/products-services/
PubMedCentral (https://www.ncbi.nlm.nih.gov/pmc/) hosts full-text for biomedical journals that don't automatically provide un-paywalled access to covered articles, as does DTIC. The one caveat is that there is an optional one year embargo for journals that aren't open access.
You can often find PDFs on researchers' home pages, and preprints are increasingly common too.
Alternatively, there is now a coalition of funders that is taken an even stronger stance: not only must research they fund be published as open access, but the journals they are published in may not hide other research behind paywalls either.
If enforced (big if), this could give an important push to making open access the default, even for places where the government does not demand it that strongly yet. However, it would help to have some more big hitters explicitly sign up, most notably the US.