You're almost right
The problem isn't that O356 is a better product, it's what you put in the last two paragraphs; there is an entrenched segment of the market that will always think they need the O365 solution, because: training. I've used both products, and for work or home Google Docs, and related services do a great job. I don't have to purchase any licenses with it, and it works across many devices. Having used O365/Skype at my last gig I can tell you this; O365 goes down, or it's otherwise unavailable, more often that you would hope. It fails to work with non-Windows browsers in little, but meaningful ways. Like it would never EVER remember my settings for Keep Me Logged In, or whatever they called it. It just lacked anything that made me want to use it instead of the desktop apps, and we had no choice in the matter. The Exchange client worked well otherwise, and had many of the same setups as it's desktop counterpart, but it was no replacement for a desktop client. Maybe 75% replacement, 25% annoyance. With my Google services the connectivity was rock solid and hardly ever had a glitch. Again, it's free. How can they do that?! I guess it's not so free if you spring for the enterprisey appliance/services, but at a consumer level does O365 have freeness built in? Let me check...nope, looks like it's subscription only, and not just a sign up with your email for free service like the Google apps/services. Plus, why the stingy Skype 60 minutes per month? Didn't Skype used to be free, for however long you were in the session? Just little shitty things like that make me avoid O365.
So, for entrenched sites that can't bear to learn any different apps, other than when their current app upgrades and forced the issue, O365 is your man. But, from a usability standpoint, and a cost standpoint, I get everything I need from the Googly apps, and I even have free Apple versions of some of that stuff to fall back on, if I don't use a LibreOffice, or other Open Office variant. Cloud is never an issue, since you can download your docs to your device, if you prefer. So, I can see why O365 is succeeding, but it's just old momentum that will probably suffer at the hands of the GWX madness that has struck Redmond these past few months. Hopefully a shift to more modern computing systems on the desktop, fueled by bad W10 experiences, will be in the future, or not. If you knew this you could make some money, couldn't you? And the segmentation of the O365 clients will help beef up the compatibility with non-Edge browsers, you would hope. Time will tell. It is known.