It would be really cool of they could update the UI of the app to the newer Android look, because app is really simple and fast, unlike the Google Music or Shuttle, they are kind off lagging on my phone
Re-read what I said originally. I've made it bold.
Google and OEM's don't ship phones with that media player. It's outdated and it's only maintained by a few for testing purposes. In fact the last change made to it was over a year ago and they didn't even bother to merge it until recently. Why? Because nobody cares about it.
The last official Android version of the music app was designed for Gingerbread. Since then they've patched it for virtual devices, but they've not adjusted it's visuals, options or updated how it functions. So like I said, the app might exist but it's not a Jelly Bean app. When you want the modern app it's Google Play Music or Apollo, depending on if you're AOSP or CM.
Apollo works best for now.