I&#x27;d have to disagree on that.
I have a note 4, rooted, stock other than that, and I just tested from unlock to opening google music to hitting play, and it took mere seconds the whole way through. 
I doubt this has anything to do with me rooting my phone, but I would also add that I have a large amount of applications installed on my phone, as well as several background processes that I run continuously.
Not only is my phone fast and responsive, but I have irregular services like complete Linux installer running Ubuntu for arm, pushbullet, tasker, unified remote, and servers ultimate pro. And when I hit play, it plays immediately, I&#x27;ve had lag before, but that was due to latency on the network and not the application itself.
Just a alternate point of view :)