This absolutely needs to become part of grant requirements. The NIH is doing well (and good!) on this, and the new German government has announced that software funded by the public needs to be free and research should be open.
In 2018, 11 European research-funding organizations formed what is known as cOAlition S with the primary objective to ensure full, immediate, open access to all publications containing research data obtained in projects funded by its member agencies. The chief premises of cOAlition S were laid down in Plan S, which is scheduled for implementation in June 2020. So nowadays when someone wins grants from these agencies he’s required to publish his results in open access.
It’s not ideal, because many people reserve grant money for open access fees but AFAIK the policy also allows to publish behind paywall as long as you provide publicly available copy in repository (institutional or public like arxiv etc). In my opinion the second option is much better (as it saves money), but not all journals allow to put copy of the article in public repos (sometimes they require that the public version is either before editor’s revisions or puts some time embargo, like a year or 6 months, for publishing final version of the article).