Yes, it is a very bad design. But it's what I've learned to expect from Apple since Cook took over. Jobs was an innovator, Cook is a businessman. Two different mindsets that affect the design of Apple products. I'm also very certain that Apple does things to our phones just before a new phone and iOS comes out. Just enough to frustrate people into upgrading to the "latest and greatest". 1. I speak from experience with dealing with Apple Care over the years whenever I have issues with my phone. Which is usually just around the time a new phone comes out with the latest iOS. 2. Admitted by Apple tech guys. All they need is the IMEI to be able to control your phone. They have EVERYONE's IMEI. They just have to "ask" your permission to access your phone. They really don't need your permission to do that. A perfect example, my 6S had 10.2.2. And because I don't update unless I absolutely need to, and auto update is turned off, there should be no reason for that to change. Yet, one day, I happened to check About, and noticed that my phone was now on 10.3.3. So my phone got updated without my knowledge or permission. Keep that in mind.
As for your issue. I found that if you watch a video on Safari, or access YouTube from Safari, but don't stop it, or close the browser window, the iPhone will continue to think you are still using the media player. That's why it shows up on the lock screen. I understand it makes it easier to access. But like you said, poorly designed. Not very intuitive at all. So this issue for me was easily fixed by not watching videos on Safari. I miss the old Apple. Where everything "Just Works".