We will improve as long as we can keep this group of players together. Out of our main group of 18 in our strongest match day squad, only 5 can be said to have reached their peak, and 2 of those are goalkeepers.
We are like a fine wine, maturing with time and age.
City don't worry me whatsoever. Pep has strengthened them in the only way he knows how, because it is the way he relied on throughout his career: on the attack. Defensively, they are shambolic and more or less need an entirely new back line (GK, CB, LB, RB). Sure, they can afford whoever they want. But Pep's handling of the Hart/Bravo situation shows his lack of knowledge about defensive strength.
Liverpool, whether they like it or not, also need an overhaul. Here again, Klopp has now had 3 windows to address their gaping flaws but has failed to do so despite massive financial backing. They need a new GK,CB,LB and DM as well as a proper out an out ST. What makes you assume he will magically get it right 4th time lucky?
It is also worth noting that of all the big 6, Pool are closest to us in terms of transfer fees and clout, especially since our recent wage hike following CL qualification. We have been scuppering their transfers for years now (Dempsey and Siggy spring to mind). So again, I'm not worried about them.
As for United. Mourinho's arrogance will remain your one true shortcoming, as it was at Chelsea. Of all the managers you have cited, he knows the league inside out back to front and was also fully aware of the flaws at United having played against you while managing Chelsea. His arrogance has led to an inherent distrust of youth and over-reliance on 'his veterans'. You are the only big club aside from ourselves producing home-grown talent. It has always been a mark of pride for United since the Busby era. Under Mourinho, that talent will rot on the bench at best.
On paper, United have the most balanced squad of the 3 teams you've mentioned. Miserly at the back, strong in the midfield and with an array of wide options and attacking talent. Of all the big teams, given the experience of your manager, you should be doing
much better than you are. Again, Mourinho's stubborn, paranoid nature will be your undoing. Ultra-conservative, mind-numbingly boring tactical choices as soon as he feels the heat (see last night for a prime example of this). These were the same tactics that got him sacked from Madrid, the same tactics that got him sacked at Chelsea. Again...what makes you think that the old dog will learn new tricks? Your performance against Chelsea proved how dangerous you are when the shackles are released. So why not play like that all season? Fergie managed it.
So in conclusion: excellent attempt at a wum, but the past 3 seasons have demonstrated that we have nothing to fear.
(Apart from playing all of our home games at Wembley

)