The answer is compulsory licensing. People have been doing that for decades. It's a solved problem. Look at e.g. radio. There's a compulsory licensing scheme for radio stations. They pay into a pool that is divvied up to rights holders based on some kind of keys and metrics. Radio stations can play whatever music they want, no additional licensing required.

We should have that for streaming music and video. Any streaming platform could offer any content they'd want to host, and they pay into a pool for rights holders. Streaming platforms would have to compete on quality, features, price, availability, etc. But not on holding content hostage.