Definitely the number of grants would go down as the cost of publishing starts being factored in, although this may be partly or fully outweighed by the reduction in universities' costs.
Universities are paying essentially all of the cost one way or another now, how could it not be fully outweighed? It would be more than fully outweighed because the universities would no longer have to pay the publishers the amount that constitutes the monopoly rent from the copyright.
Meanwhile the public gets free access to the research which increases its utility.
2. There are many places to put extra money in a university (add to endowment, expand, etc).
>It would be more than fully outweighed because the universities would no longer have to pay the publishers the amount that constitutes the monopoly rent from the copyright.
Why do you think profit margins would go down? The "rent", to the extent a 30% margin is rent, is from the need to publish in prestigious journals. Copyright just affects how that rent is collected, but it's not clear to me how that would reduce the rent. (It may go down because people become more hesitant to publish due to the increased cost which forces them to lower their price to get more papers. But that wouldn't be such a good thing.)
Regarding profit: sure, you could set up a nonprofit to do the same job. You'll end up reducing costs by 20-40%, even assuming you don't have higher costs because of lower scale/lack of experience/etc.
For other essentials like food, I've seen stories about nonprofits that get large groups together and buy in bulk. Co-ops are basically the same idea. Using a non profit to reduce costs has been done.