I've used similar
but prefer the "landlord" analogy.
Yes, it's your phone. You have rights - but...the landlord can always get access and you're not allowed to paint all the rooms black, whilst smoking crack.
Now you probably don't have the narcotic/decorating urge - up until somebody tells you you can't. Then you get pissed off.
On the flip side you could root your phone/buy your house and do whatever the hell you damn well please - but you've forfeited the right to demand somebody else fixes the heating when it packs up/install google's new pay app.
Defending the poor google underdo seems a bit strange, but I can't help feel that they'd like as many people as possible to use their app, and if they block people from doing so, they've probably got a carefully cost-analyzed reason.
Don't like it? Don't root, or write your own pay app.