That’s the thing, though. I respect the analogy, but the equivalent here would be if the game was also checking your drive for other games, for financial apps, scanning your browser’s cookies to see which sites you visit, etc.

If, while playing a singleplayer game, they’re recording what actions you take within that singleplayer game, it’s understandable some people wouldn’t even want that - but I also don’t see that as nearly so invasive as other data travesties. Worse, highlighting it here feels like a “cry wolf” situation where you’d desensitize people to the most harmful privacy breaches.

Again, I don't doubt that you do not see it as an incredibly invasive thing. I'm lamenting that you (and many) don't.
You're doing something on your computer. Locally. In your own time. With a thing that is - ostensibly - yours. Why is it even remotely acceptable that some corporate entity is watching you over your shoulder while you do it? I'm running out of words to express how nuts this seems to me.

The bastard!

More like, if you purchased an electric clipper, and it wirelessly sent a message to the company every time you used it, to let them know how long and where you're using it.

They already have purchase info, they don't need usage info. At least not for free with out the consent or knowledge of the customer.

We need to know your personal grooming metrics, you can opt out if you create an account.

I’d say it’s more like your hairdresser tracking how long you are in their store and what haircut you get- but you do you!

I'm not married to the analogy, just totally flabbergasted that "Using your own software on your own computer when and how you see fit without being watched" appears to be a slightly controversial aspiration for no (to me) apparent reason. Evidently I'm missing something, not explaining myself very clearly or both.

I’m sorry, but that’s a terrible analogy. In the gaming scenario, Ubisoft is collecting the data on their own product usage

Well, in the corporate software-as-a-service insane troll logic hellscape in which we live that could indeed make sense. Mind you, that's not meant to be a rant against you but against the fact that this train of thought has indeed been completely normalized.
In the fantasy world of the past into which I'd like to go back to live happily it is precisely not Ubisoft's product. It's mine. I bought it - none of what I do with it is any of Ubisoft's business. The business transaction has been concluded. If they want to know what I do with my game then they can ask me nicely about it. I'll certainly not allow them to install a proverbial camera over the executable.

It's not a good analogy, I agree, but I'm too angry to come up with a better one right now.