Yes, I definitely want "Shockz" to be able to run background daemons on my phone for proximity pairing and god knows what else a fly by night OEM might want to do. That would make my phone work much, much better.
That concept is entirely foreign to me, as an Android user. Closest I've come to being "forced" to install anything is when I need a boarding pass, and even then I'll often use a screenshot from my desktop. I can't think of any other mandatory apps on my phone right now.
Out of curiosity, why quote Shokz and then spell it incorrectly, as well? I gather you're not a runner, so you have never heard of them, but I'm confused as to what you were trying to convey.
Damn, if only we had some form of technology that would let a user allow or reject access to system APIs. Sadly this is impossible and cannot be implemented.