YouTube website is not a replacement for a web app, and anyone who used the app on, say, Android would know. The most basic thing I expect from any YouTube mobile app is being able to play things in the background. Mobile browsers don't allow websites to do that, and for very good reasons.
As for "don't conform to Terms and Conditions" ... well, if you guys don't offer an API to build a conforming app, then such a complaint is misleading, because there's no way to build one. So what you're really saying is that you will block all apps except your own, or made with your blessing. And then we're back to square one - your refusal to grant such a blessing to an app on a competing platform is abuse of your monopoly position wrt YouTube.
Mobile browsers do allow that, YouTube just breaks that functionality for reasons unknown. They do it on mobile only as well, videos do play in the background when I use the desktop site.
And the reasons aren't that unknown - if I'm not mistaken background playback is one of the selling points of a Youtube Premium (formerly Red) subscription.
As for "don't conform to Terms and Conditions" ... well, if you guys don't offer an API to build a conforming app, then such a complaint is misleading, because there's no way to build one. So what you're really saying is that you will block all apps except your own, or made with your blessing. And then we're back to square one - your refusal to grant such a blessing to an app on a competing platform is abuse of your monopoly position wrt YouTube.