360 ushered in a shit load of new stuff and not all of it was good. You get DLC and smaller downloadable games on console, party systems and the like, but the horse armors and paid online and everything came along with it.
I'd argue that Microsoft has never had a big enough game full of microtransactions to have really been "at fault" for them, let alone normalizing them. I'd lay that on the likes of EA, Blizzard, Rockstar, Valve and mobile games in general. The EA card stuff in their sports games, Overwatch loot boxes, GTA Online's grimy paid currency, Valve was doing hats in TF2 nearly 10 years ago. Games like Farmville were normalizing gross microstransactions to a wide audience, again nearly 10 years ago, well before anything to do with fucking Ryse. Now Fortnite has made $20 skins and obscenely priced emotes a totally normal and acceptable thing to millions and millions of kids. They're here forever.
Like, yeah, Microsoft absolutely opened the door by pushing a lot of things forward with Live, especially on 360, but I don't know that they specifically "made videogames bad" because they've never been the ones to push that shit. They are absolutely at fault for whatever future damage game subscription services may cause though.