A superior manager would have his available players performing better than the sum of thier parts.
As much as I agree with that, over the course of a season, quality is still the sine qua non. But by quality I don't just mean the goodness of each of the parts, but also having the right parts at hand - ie. the right balance. For example, Saudi Sportswashing Machine did great last season with a poor man's Modric in Cabaye (still a fantastic player mind, just not Modric).
I think every team needs a passing type, a tempo setter, someone who always wants to keep possession and is constantly moving to make themselves available for the pass - even if they're not that amazing at this role, a la Joe Allen. But just having this type matters. The problem comes when every midfielder is more of a mover, someone who might touch the ball 19 times per game since they're more interested in taking up the right positions in anticipation of being released, or sweeping up rebounds/scuffed balls. Bale, Lennon, Dempsey, and Sig are of this type. Sandro prefers to win and then give the ball to his partner quickly. Dembele is a hard-worker with the mind of a "mover" - he'll tackle and win a lot of balls, but his instinct is to dribble and hang onto it to go forward like an AM, rather than set a metronymic passing tempo both vertically and laterally.
We are gravely lacking in passers in general, not just creative passers. Both Modric and VdV (and indeed Parker, despite his lower creativity) routinely had 70+ passes per game last season - helped, no doubt, by an in-form Ade's presence, but they are also natural passers who like to knit together play. Without them we are panicking in possession. Without them we don't have the ability even to hold on to the ball for most of a game under pressure. Yes, it is possible that lots of coaching on team movement will make up for this issue of technique and natural inclination, but that is going to take a long, LONG time.
Over the course of a season, I think that no amount of coaching will solve our deficit in terms of key qualities that we are missing - not overall quality, but the key type of player. It will paper over the cracks, but over the longer term, there is very little the manager can do when our rivals can buy all of Oscar, Hazard, Mata etc while we have to make do with Sig. This is what's happening to Arsenal, despite having a brilliant coach (note I said coach, not tactician) who has been there for years and years to establish his style. You don't always get what you pay for, but with the market evolving the way it is, it's getting harder and harder to convince someone who's even remotely talented to join us rather than get paid more to sit on a guaranteed CL team's bench. So the only real long term solution is smart investment - we can't just coach ourselves out of a billion-dollar gap when money (and the accompanying success) is all that matters to almost all players, and we can't just spend like crazy either. I don't know where we'll magically come up with the money, but, hey - we have plenty of deadwood, and just buying one player the manager genuinely wants like Moutinho would be a great start