No, you’re forgetting the already existing (ie has since iOS 4, but the exact implementation has changed over the years) system play/pause/ff/rewind commands. While they’re maybe not as convenient as having them right on the home screen if you happen to be in the home screen, they’re just one swipe away in Control Center or Notification Center whether you’re on the home screen or in another app. And if you’re on the lock screen, it’s front and center.
I don’t really get sticking music controls on the home screen if they happen to be one swipe away everywhere. It’s not like I spend a bunch of time just staring at the home screen, and you’ve got the issue of swiping up to try to find them only to realize they’re on a different page of the home screen.
As for Android’s implementation, I wonder how many Android users really use widgets, least of all widgets that aren’t part of the stock UI? And not all launchers support widgets, I know for a fact that the Google stock TV launcher doesn’t support them, as that’s the UI I use on my one Android device. For some reason, I get the suspicion that most Android users don’t really understand how the home screen works. (People have this stereotype of Android users as tech savvy people who’ll modify every aspect of their system, but most of the ones I’ve met have an Android phone because it’s cheaper, and they don’t really get why you’d want a smartphone except maybe for the camera/email/maybe web browser or social media apps.)