I haven't climbed Mt Blanc. But I climbed (and guided on) other 4000m peaks in the Alps.
Going without rope on a glacier is a bad idea. I assume that you can see a lot of bad stuff on the Gouter Route, but that doesn't mean that you should join in. Bring a friend along or pay somebody. And don't be one of them:
https://www.petzl.com/fondation/projets/accidents-couloir-gouter?language=enI often venture solo in the Alps, but having felt the void under my feet on a glacier more than once (roped up), I am really careful with glaciers and consider the ones high up no-go-zones when soloing.
Check out the prices for private tours. I just organised one in the Alps and it was cheaper than the official guided group tours (which take a day longer and climb some more peaks). With a guide you might also have the possibility to climb Mt Blanc on a more interesting route with less people.