It's intentional, people (mostly of the younger generation) were using the Youtube app as a free music player. Also, as someone else mentioned it prevented them from showing ads.Is it so difficult for them to add audio continues play outside the app.......?.... the most requested feature.
Actually, since their recent change involving HTML5 (not sure what they did), I remember seeing ads a couple of times because their player somehow loaded instead of the built-in QuickTime player on iOS. It might have been on the iPad only because I still see the QuickTime player without ads on my iPhone.
The latest version of the HTML5 YT player mimics the Flash Player perfectly including ads, even when embedded. This new player (V3) is not using the standard QT controls and doesn't currently work for Picture-in-Picture in iOS 9 for example. Sites can still embed YT videos using the old player (V2) that does provide standard QT controls (and PIP for iOS 9) but it's being phased out.
And while the YT app doesn't work for PIP in iOS 9 currently because it doesn't use standard controls, Apple provides APIs to enable third parties like Google to add a custom PIP button for their custom player, which they will hopefully add for the iOS 9 version this fall.