Apple is not going to block YouTube. When Apple said they were going to drop the YouTube app they also announced that Google was working on a YouTube app that would be available in the App Store. Obviously they didn't just drop a bomb, they talked it over with Google first and the result was an agreement, not a continuation of the battle being fought in other areas.
Apple had some kind of licensing agreement with Google that allowed them to include the YouTube app in iOS. Understand, this agreement predates most of the third party support Google has included since the advent of iOS. For whatever reason Apple is not renewing the license, or Google won't renew it, I"m not sure which.
Apple wants to lessen it's dependence on Google who has increasingly become a rival because of the Android ecosystem. Google can and has limited Apple's access to Google's services; like with turn-by-turn in the Maps app. Google on the other hand wants full control of how it's services are presented, mostly the ability to present adds and collect data. Apple won't block Google, because it's too important a part of the internet and would cost them customers. Google will support Apple products (though maybe not as well as Android) because their users represent a huge portion of their profits in advertising.
Both Apple and Google are getting what they want with this move.
It remains to be seen if the Google YouTube app will be better than the mobile site; which was already better than Apples app as far as I'm concerned, even with the adds.