Would it be better if youtube removed the free, ad supported version entirely, and only allowed paid users?
yeah, as it would open up the market
It would be better if there was a better value proposition, instead of “pay to get what we removed”.
It’s not as though free users listening with the app in the background is somehow an additional marginal expense as opposed to them listening with the app in the foreground.
There is no free Google product. You pay for all of them with your data, your privacy, and your attention.
Your data is worth far more to them than a $13/month subscription fee. In fact, if you do pay it, the data becomes even more valuable, because you're now guaranteed to always be logged in. You're also likely to use it more to get more "value" out of your purchase, generating even more value (for them). Finally, you've also identified yourself as the kind of person that pays for things that should be actually free.
Worse than all of this, when you use Google (or any of these malware/spyware companies), thanks to network effects, you don't just pay for it with your freedom, you pay for it with some of everyone else's too.