Well, you can read his views on monopoly here. I would say some of the following is edgy, in that he's saying that (at least temporary) monopolies can be socially efficient (not just that the companies "want" to be monopolies):

Monopoly might net incentivize innovation. If a company creates something dramatically better than the next best thing, where’s the harm in allowing it to price it higher than its marginal cost of production? The delta is the creators’ reward for creating the new thing. Monopolistic firms can also conduct better long-term planning and take on deeper project financing, since there’s a sense of durability that wouldn’t exist in perfect competition where profits are zero...

Perfect competition might also seem to make sense because it’s economically efficient in a static world... The deeper criticism of perfect competition, though, is that it is irrelevant in a dynamic world. If there is no equilibrium—if things are constantly moving around—you can capture some of the value you create. Under perfect competition, you can’t. Perfect competition thus preempts the question of value; you get to compete hard, but you can never gain anything for all your struggle. Perversely, the more intense the competition, the less likely you’ll be able to capture any value at all.

But what's "edgy" and what's "mainstream" is a matter of perspective. Thiel is influenced by Austrian economics, and this sounds like something out of Schumpeter, or maybe Hayek. To someone familiar with those ideas and concepts, this is hardly startling insight, but many people really do have the prejudice that all markets should be perfectly competitive at all times.