You're so wrong that not only will Xbox clearly be going this route, but Sony will 100% follow suite as well. I don't even put Nintendo off the table on this.
It'll be a little green icon that you can load up on your phone. It'll have cloud versions of everything you've ever purchased, plus all GP content and mobile content. It'll have their own store integrated into it. Or you can load the same thing on any capable PC or any of the various handhelds and download local copies to play offline. Or play it on TVs, browsers, anything.
The only branding they need is "green." It's a little green icon. Netflix is a little red icon. Doesn't matter that it isn't DVDs anymore. Netflix is now games, movies, TV shows. The point is its going to be everywhere. Sony is literally already porting most of their stuff to PC.
Your comment about "people not understanding the industry" is going to be funny when you're 100% wrong on everything you're claiming. I genuinely think a lot of people that only game on PS are about a decade behind in terms of realizing what is happening. You guys still think they're going to making discs for you forever.