There seems to be quite a few available for music. Using apple music, spotify, tidal or whatever else doesn't seem to have the exclusivity problems that TV equivalents have.
I can probably count the number of exclusive artists to each music provider on my hand.
They're trying to recreate the cable TV channel package model on the internet, because it's a mechanism for price discrimination.
If you make twenty shows and you want to sell subscriptions a la carte, how much do you charge per show? If you charge $10/month per show then you lose the business of everyone who might have paid you anything even slightly less than that. If you charge $.50/month per show to get those customers, you lose $9.50/month from everyone who would have paid $10/month per show. But if you put all twenty shows together in a bundle and sell them collectively for $10/month, you get $10/month from everyone who values the collection of shows at $10/month or more, regardless of the value they place on each individual show. Which can turn out to be more money.
But that is less likely to work in a more competitive market. People only have so many hours to watch television. It may be worth $10/month for a package of shows to get the one you really want when that's the only option, but when someone else is offering an equivalently good show a la carte for $10/year and you don't have time to watch both, people will choose the one that saves them $90/year worth of shows they weren't actually interested in.
The broader problem is that without a distribution monopoly to use as a chokepoint, content creation is a highly competitive market, and highly competitive markets have low margins. So the incumbents are flailing around trying to find something that looks like the model they're used to, even though that model is now defunct.
The model which is likely to out-compete a la carte is the one where content producers make non-exclusive licenses to multiple aggregation companies that sell flat rate plans to their customers. Because $10/month for twenty shows can't out-compete $10/year for the one show you actually want anymore, but $20/month for every show can.
This is actually untrue: Jay-Z and Beyonce's new album is Tidal exclusive, and I just saw someone complaining about it on social media today. I'd expect this trend to increase, not decrease, over time.
There are laws that set statutory royalty fees for music recordings, which strongly encourages non-exclusive licensing, even when those laws don't apply.
I can probably count the number of exclusive artists to each music provider on my hand.