I don't disagree with your examples above (and btw I am not talking about any of this in relation to Frank, just in relation to xG theory), but I am disagreeing with "the stats are often very blind". As I've said before, it is a fact that the highest positive difference in xG every season will finish very high in the league, and the highest negative XG will finish very low in the league, so xG is definitely a good proxy over a reasonable timeframe for 'is my team playing well enough to score lots of points', or something akin to that. I'm not denying that there will be outliers, whether they are caused by playing style or particular players etc, so the stats will (to use one of your terms) 'occasionally be blind', but I do feel that you aren't giving xG sufficient 'credit' generally as a proxy for playing in a way that over time will get you lots of points. (Apologies if that's just my misunderstanding of your thrust).A lot of it is so easy to be corrupted by the players in the system though.
You could put the most attractive footballing team together and stick this version of Kolo Muani at the top of it. If he's dawdling with the ball, passing it to no one, or losing possession when it would be a high xG shot if only it was taken, it's chalked off. If a player is judged offside, the xG is chalked off. If the referee blows for a foul that wasn't in the play leading up to it (e.g. someone like Romero deciding to push someone off the ball), it's chalked off.
It isn't really a black and white thing, but I just mean that the stats are often very blind.
With Kane and Son in this team, I honestly believed we'd comfortably have dug ourselves out of most of the holes here and be somewhere around Liverpool in the table right now. We've not been playing anywhere near as badly as we did under Nuno, and I wouldn't say the players look as lost as they did under Stellini, but they are simply putting in poor performances.
I still think people would be calling for Frank to be gone though as football is like politics these days, where people want good looking charismatic leaders, even though it's basically nothing to do with the job they do. There will be people who always decide they don't like the manager and nothing else will matter (see: Sherwood).
I would repeat, size 72, bold, underline - my position isn't defending the current manager, but is quashing the idea that the ones that came before were all that much better. Not only is this guy the first in over 10 years to not have Kane/Son, but he also doesn't have any of the replacements either, so we have to wonder how long any of the others would have lasted with some of the donkeys we have up front, because we can see with our own eyes that there's low xG because of players doing dumb things in the final third.
If you're saying that Frank's particular situation is such an outlier, or can't reasonably be compared to those of our previous managers, for whatever reason, then that's fine (well, it's a different conversation which I'd be happy to engage on separately to this one), but the overall xG theory is both useful and significant, and I'd expect someone like you to give it proper credit (and perhaps you do, perhaps you've just been a bit flippant / overly general here with your assessment of xG, or perhaps I've incorrectly interpreted you that way).