Interesting theory. And kudos for doing the work and verifying with stats.My thesis is that there's a shift in risk/reward depending on the score, which mean it's better to attempt more risky defence-splitting passes when trying to establish a lead, which is going to mean lower possession stats because they don't always come off. Then after establishing a lead, risk/reward favours safer option when in possession, which leads to higher possession%. So let's test the hypothesis on City's last 10 or so EPL games:
There does seem to be a slight correlation but my suspicion is there's another side of the story which might work against it: when teams are either winning or drawing against City, they're happy to cough up possession and just sit in the low block, protecting the lead. When they go behind is when they need the ball; it's no good just letting City pass it around their centre backs the rest of the game.
So you're left with two competing narratives: City's increased willingness to play the safe pass when ahead, leading to a higher possession %, versus the opposition's greater desire to win back the ball, lowering City's possession %. I suspect that might be in part what is causing the lack of a clear relationship in your analysis.
Agreed. To add to that, I'd say (from the eye test) that we tend to try and force it through the middle a lot more than City, who often just play with one player in the middle and are much happier to pass it round the opponents.Anyway, coming back to the main point: Tottenham's matches with high possession% and low chance creation (Leicester, Newcastle, Coventry) are symptomatic of insufficient risk-taking when in possession, too often opting for safe passes around the horseshoe, and not enough attempts at defence-splitting passes, take-ons, disguised flicks etc.
See this still from their Ipswich game:

How often does our build up look like this? With the middle of the pitch basically surrendered to the opponent, bar two players (Kovacic and Lewis, who aren't looking to receive the ball at all because they're outnumbered 5 to 2)? Barely ever.
Gvardiol as a LCB is an obvious formational change--in our system he'd be high and inside, probably somewhere near Doku, and that again forces us to try and play it more centrally as opposed to going around the opponent. It also allows the opponent to sit more centrally.
But what's striking to me in this image is how both KDB and Doku are outside the opponent's block (and Savio too on the other side). Look how spread out everyone is, everyone looks at least 10m apart, and how spread out it it forces Ipswich to be as a result.
Unsurprisingly here the ball goes out to Gvardiol, then KDB who's in acres of space, and City create a good chance.
Now compare that to us in build up:

Everything is much too narrow, allowing Everton to condense the play. The players aren't well spread out; Porro and Kulusevski are practically on top of each other, and the pass isn't on to either.
Ultimately everything in the way we set up is geared towards passing (read, forcing) the ball through the middle. The ball has gone into the middle, to Bissouma, who tries to force it through a pack of Everton players and it gets easily cut out. This exact sequence happened again 5 minutes later.
Back to your point: I agree with you that we suffer from lack of risk taking. But our problems in settled possession are deeper than that; it's not that the pass is on and we're just not making it. It's often that our structure is all off to begin with, and clearly there is an instruction to try and move the ball vertically and through the middle whenever possible.
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