I have to disagree with you on this, there is no way United are as far away from challenging Chelsea for the title as Liverpool or Tottenham. I won't go into the reasons why because frankly there is too many and the league table tells the story anyway.
Regarding Arsenal, personally think they are close need 2 quality additions in key areas but that could be done in this window easily if they pull their finger out.
Finally I think you're wrong about City, their squad IMO needs a lot more work than both United and Arsenal, plus they are going to struggle badly with FFP which won't help. They have an ageing squad which needs quite a lot of investment. I'd say personally United are probably 3 key signings away from challenging next season, midfield, defence (CB,RB) and maybe even 4 (goalkeeper) if De Gea goes.
That's a heck of an assertion considering Utd barely squeaked home in 4th last year which had as much to do with how poorly and how much of a backward step Liverpool, Tottenham and even Everton took IMHO as it did Utd improving. Heck, from the win at Anfield on Utd held the door WIDE open just begging Liverpool to jump back in. The fact they didn't tells far more about their disgraceful late season attitude than anything. Take De Gea out of the equation, and Utd are struggling to make the top 4 even with the other 2 being in such a putrid state last year.
Don't get me wrong. I aren't for one minute suggesting Liverpool and Tottenham are anywhere near challenging. But when I say Utd are as far away it's precisely down to none of the three are going to be coming close any time soon all things being equal. As you so pertinently said, the league table tells the story and that's a 6 win swing from 4th to 1st.
Arsenal still desperately need a goalkeeper, a dominating ball winner in the middle, and a consistent #9. Not to mention reinforcements at the back which is still the weak link. On their day, they're still as good as anyone if not the best team in the Country. But those days don't happen enough over the season on a consistent basis.
City should be solid by slowly rebuilding the next few years. They only need to add 1 or 2 marquee signings each term. The bulk of an albeit ageing squad is still only around the 29/30 YO mark. And they're putting themselves in a great position as regards FFP. Even more so if they want to stand up and challenge UEFA. Debts completely wiped out. Totally self sufficient. Wage bill slashed. The new TV deal slashing their working deficit. Off load one or two of the high earners and they should be well within the confines of whatever UEFA decide for the new FFP limit.
It'll be interesting to revisit this at this time next year, but as currently stand, I can't see much of any change to how things played out last season.
You might be right and Utd may be turning it around. I just think your personally letting your heart rule your head and you're not nearly as close to Chelsea (as much as I hate to admit it because I have for more dislike for them than yourselves) than you believe you are.