Competitors were actively licensed at the same time as SpaceX, the British government (and probably some other governments) is also actively funding competitors, and the US military has made statements that leads me believe that they plan to as well. Rather than handing them a monopoly, it seems like the governments of the world are doing everything reasonably possible to create a competitive market.

I'm not sure it will succeed, it's a "natural monopoly" type of market (high fixed cost, low marginal cost), and SpaceX has an incredible advantage in being really frickin good at launching rockets (though they do offer to sell those services).