Someone needs to rent and service the servers, update the software, bandwidth costs money, etc..
I'm absolutely convinced that if copyrights weren't an issue, there would be enough governments, foundations, universities, corporations, and individuals willing to pay the costs of making scientific publications available to everyone. It wouldn't have to be a paid service.
Scientific papers use approximately zero bandwidth.
As a point of reference, if I hosted such a website on my home internet connection I would be paying approximately 0.00013 cents per upload. Even users downloading millions of papers would cost me less than a coffee.
Setting up and managing a proportionate payment system would cost more than just eating the bandwidth costs would.