On that, I entirely agree. Full-time Tim's actions last season (undermining AVB before the United game) and his evident power over Levy are both things that make me uneasy. But what we can we do but support him? He's in charge now, the least he deserves is a bit of time, even if you don't think the previous coach was given enough of said time.
In terms of chance creation (the last bit of your first paragraph), we weren't able to get shots away under AVB either because...you guessed it, because there were too many players surrounding the shooter and he had no one to pass to in an advanced position because AVB insisted on everyone staying back in case the attack broke down. The point I'm trying to get at is this: under AVB, this crowding out of the shooter tended to happen outside the box, meaning we had even less of a chance to score because of the distance to goal. Under Tim, it's happening inside the box, which gives us a greater chance of scoring just by the closer proximity to goal. Sure, it requires a bit of skill to get the shot away, but these 'top-class international' footballers couldn't control anything today, and when compared to the first touch under pressure displayed by, oh, say, Coutinho when he scored the first goal today against City, it is clear that they are either rusty or just not very good to begin with. Probably the former. Hence, if they just controlled it a wee bit better, we probably wouldn't be having this conversation.
And, as an addendum, I believe Tim is fully aware of what you're talking about (our players getting crowded out). Our faster passing and more direct approach play is geared around getting the ball to our strikers quickly, giving the opposition less time to react should they bring it down and turn towards goal and also allowing fewer opposition players the chance to get back and crowd out the shooter than a more measured, slow approach (a la AVB). So, in that sense, it is being rectified.