>PLoS [...]
At low costs of $2k~$3k per publication[0]. Elsevier closed-access journals will charge you $0 to publish your paper.
>Elsevier makes over $3 billion dollars with the closed publication model.
Elsevier is also[1] moving to APC for their journals because is better business.
>The Institutions often do not supply access to the general public despite the papers being produced with public money
Journals (usually) forbid you of sharing the published (supposedly edited) version of a paper. You're allowed to share the pre-published draft (see arXiv). Institutions could (and some indeed do) supply those drafts on their own.
>Paying the cost upfront from the grant increases the availability to the public.
At the expense of making research more expensive and hence more exclusive. It's money rather quality that matters now. Thus it isn't unsurprising that Frontiers & MDPI, two very known open-access proponent publishers, are also very known to publishing garbage. It's ironic that once was said that any journal asking you for money to publish your paper is predatory, yet nowadays somehow this is considered best practice.
[0]: https://plos.org/fees/
[1]: https://www.elsevier.com/open-access