The thing about evolution is that it just happens. That's a great truth. "Just" is very important there: no-one runs it, guides it, oversees it, directs it or invents it, and it has no goals of its own. Evolution is a completely natural process that will take place as long as three conditions obtain: that life exists, that heritable material can miscopy, and that the environment is subject to change. Extinctions happen for many reasons but they do not drive evolution. An extinction, in one sense, is a dead end, but, who knows, the ancestor of the extinct being may still be there. So might the ancestor of the ancestor, come to think of it. If some brave soul has ever put a numerical limit on the number of species that can exist at any given time, well I haven't seen it.