Just looking at Gmail now, there actually isn't a Gmail logo anymore. There is a Google logo that I can't click on and there's a Gmail link underneath it, but clicking the Gmail link opens a popup menu. I have to then click "Gmail" on the popup menu to get to my Inbox. (Or I could just click "Inbox" of course, but that sometimes gets hidden when i have a lot of labels open, and it's a smaller, fiddly link). I'd bet more people will have noticed this change in behavior than those who've noticed the change from a Gmail logo to a Google logo.
My point is, all this requires me to think. But before I could just swing my mouse into the top left corner, click "Gmail" and always end up at my inbox, no matter where I was in the application. This consistency has gone.
I should have phrased my question: "What possible advantage does this offer, to the user?"