The world would benefit much more from him starting a worthy alternative to YC. Few others are in a position to do so. He probably thinks there would be no profit in competing against what he sees as YC's monopoly.
And of course, for some kinds of businesses, one of the real competitors to seed funding is bootstrapping.
PG's "don't worry about competition at all" rings true by bringing Thiel in and allowing a competitor in a way see how a top performing product runs on the inside.
Who says Thiel isn't just gaining more knowledge to start another one later, then YC and Thiel can have a federation.
Following your reasoning there should be no tech startups and everyone should join Google, Facebook regardless of the particularly of each business/industry. Not all incubators/accelerators are targeting the same demographics. Thiel could create one that is completely orthogonal to what YC is doing as of today.