The alternative business model that the world is moving to is Open Access. The difference being that instead of paying to access the journal or paper, the researcher or institution that wishes to publish pays up front to have the paper published.
Open Access has its own problems, such as predatory journals, where researchers who don't know better or who are desperate to publish are more or less lied to as to the reach and validity of a journal. It has become an area ripe for a new kind of scammers. This has prompted efforts such as Think, Check, Submit[1].
There's also the problem with raising the funds to publish something as Open Access. It's not always the case that the researcher actually has the means to pay for Open Access.
Nevertheless, Open Access is clearly the way where the research community is headed, and we're going to see a steady growth in percentage of research published as such over the next decade or so. But it does come with its own set of problems to solve.