Youtube is successful and even dominates the space, but is not a monopoly. There are other video hosting services that can be accessed by anyone. You can start your own if you think there's a need. The fact is that people like Youtube.
Monopolies have a specific lock on their customers or their supply of a limited resource. That's why people are okay with breaking them up. Not just because they're really popular and successful.
What if Bic and Mead said you can't write a opinion that we don't like using our pen and notebooks?
Bic and Mead don't host your content. You buy their tools to create your own content and then publish it yourself, give it out yourself on media you paid for, etc.
What if US Postal Service said you can't send a snail mail if it contains references to UPS or FedEx?
The USPS is a government-supported entity. Special rules apply for entities that have government laws behind just them.
If a delivery entity opened your packages to evaluate content, that would present an entirely different sent of problems for them and their customers - because the content is private. Youtube videos are public. That's the point. Youtube has determined for their own reasons that extremist content hurts their business model.