Another update from me. As per the experience of others, my brand new installation of Windows 11 yesterday worked flawlessly till the moment I plugged the XBox controller in. Literally, the very next time I re-started, the error message was there. Thankfully, the published work around on the net does work (to disable the gaming input service). And it definitely does not seem to make the slightest difference to the performance or the functionality of the controllers I have at all, apart from getting rid of the error messages. I sit a bit easier if a workaround simply involves doing something I can achieve through the Windows 11 user interface. If it meant getting more deeply under the bonnet, I would be more worried about the consequences (I am finding when it comes to Windows 11, it is best not to too too much DIY under the bonnet (hood for you in the US :) and instead just go with the flow lest the next forced update breaks what you did and makes things far worse. Not like the old days when we had total control over what updates we accepted from Microsoft.
I have thus decided to stick with this workaround and if Microsoft comes around and breaks the workaround (or breaks something else entirely), I will deal with that when the time comes. Life is too short to be afraid of Microsoft updates that break things!!
Incidentally, I am not counting on a fix anytime soon - the drivers that were loaded when I installed the controller last night were dated June this year. Given this issue has been around for more than 5 months, if Microsoft were going to fix it, they would have already. I suspect the answer is that firmware updates are required for Xbox controllers in order to properly fix this which puts the ball in the hardware vendor's court. And since many of these controllers are quite old (but perfectly good as in my F710), I am not counting on firmware updates either. Logitech probably had to be dragged kicking and screaming just to put out a Windows 10 driver for this product!
I wouldn't be the slightest bit surprised if Microsoft in a future update make this game controller service one of those services that is impossible to disable!!