There's no doubt Alexis is a special player. There are very, very few players who can generate such a large goal threat from a wide position: he ranked 6th in Shots per 90 in 2015-16 and scored 13 goals, a mark bettered only by Mahrez in terms of non-strikers. However, that excellent record is at least slightly tempered by his Usage Rate, which shows Sanchez used more possessions than any other player in the league that year. In terms of generating shots, assists and key passes per possession used, Sanchez ranked just 6th on Arsenal. That high of a Usage Rate makes it clear how much he was the focal point of Arsenal's attack in 15-16, and as a result that puts his efficiency numbers in a somewhat better light (after all, if you're the primary focus of defensive effort you're less likely to perform well). There's little doubt he would provide more goals from out wide than Sterling or Sane could (the latter had fewer shots per 90 than Kolarov last season), if not from simple shot volume then from the fact he can actually hit the ball with his laces. If City were getting that vintage of Sanchez, I could see an argument for it.
The problem is, of course, that I don't think we are. For one thing, Alexis played primarily as a striker last season. While this led to his highest goal total ever, his Usage Rate and % of possessions with a positive outcome were very similar, and Sanchez greatly outperformed his xG. Also, as I wrote in an earlier piece, playing as a striker reduced the effectiveness of Ozil and the Arsenal attack as a whole. City have one and possibly two strikers who are better than him, so it would make more sense to put him on the wing, where he excelled previously. That of course would stunt the development of Sterling and Sane and replace the one position where we have starters below peak age with a 29 year old. There's also the fact that Sanchez played over 3000 Premier League minutes last season and is well-known for never wanting to rest. Combined with a playing style that is highly dependent on his legs, I think it unlikely he will age gracefully. You can argue that he will have reduced minutes in this City team, and I think he would were he to join, but that's not what his pricetag is going to be based on and his track record of wanting to play literally all the time suggests he will have trouble accepting that.
So why do City want Sanchez so badly? As far as I can tell, the answer seems to be balance. Indulge me a dive into the subjective here, mainly because I don't have good statistics for this, and let's break up City's attacking personnel into three broad categories based on how they primarily generate shots: passers, runners, and dribblers. Right now, I would say City have passers (Silva, KDB, Gundo, Toure) and runners (Kun, Sterling, Sane) only. Sanchez is a dribbler, something City didn't really have until they picked up Bernardo (yes, Sterling and Sane both dribble a lot, Sterling more than Sanchez on a per 90 basis actually. Still, their ability to latch on to through-balls from KDB and Silva bigger part of their value). I think Pep wants to have more people who can create their own shot off of the dribble on both wings as an option, particularly against teams that set up in a deep block that is hard to break down. Sanchez could definitely help accomplish this goal and Pep may believe getting him is necessary as a result.
The price of that would mean a drastic restructuring of the attack though. City's Usage Rates last season look like this (minimum of 1000 minutes):
|Player||Unsuccessful Passes||Key Passes||Assists||Goals||Shots||Unsuccessful Take-Ons||Minutes||Possessions Used||Usage Rate||% Positive|
Right now, Silva and KDB as passers in the advanced double-pivot below the striker take up the majority of possessions. Surrounding them with runners like Sterling, Kun, and Sane gives them good options to pass the ball and helpfully allows those players to be involved without the ball at their feet as much. Sanchez would throw a wrench into that. His Usage Rate is higher than anyone on the City team, at north of 18%, and he had a high percentage of Arsenal's unassisted shots. As Ryan O'Hanlon pointed out, he is not one to take shots directly from a teammate's pass, rather he gets the ball outside the box and then moves in to shoot. That doesn't fit with a team based around incorporating two high-volume passers from just such an area, particularly when he was unable to click with similar players (Ozil in particular) at Arsenal.
There's an argument to be made that it doesn't matter if Sanchez can replicate his previous form, so long as he helps City win the title. I would agree that the marginal value of a point is greater to City than it is to a midtable team like West Ham (another reason their transfer business was so weird). However, I think that argument fails to address the reasons why City didn't meet expectations last season though. In terms of xG, City had the best figure in the league. While we didn't overperform by G-xG, we weren't vastly undershooting. You could argue that City should have created more with the possession we had (City were just 8th in SOT/Possession), but still the overall results were quite good. Where we underperformed was in defense: Bravo obviously was a factor (after a decent enough start, in one six-week period he conceded 64% of the shots on target he faced), but there were also some systemic issues. Benjamin Pugsley has shown that City tended to have few defenders in the box when opponents' moved the ball there, which is a pretty good indication there was less defensive pressure applied. The additions in goal and at fullback were aimed to address these concerns, as the pace supplied by Walker, Danilo, and Mendy ought to allow them to get into position more easily when the ball is lost and still contribute to the attack. However, there has been no indication of City signing a central midfielder to play at the base of the formation, despite Gundogan's injury issues and the age of Fernandinho & Toure, not to mention the defensive limitations of the latter. That to me would be the area City need to address most urgently. The surplus value of Sanchez over the players potentially replaced by him is nowhere near what the value a top-class CM could provide, and that's before considering how Sanchez would necessitate a restructuring of the attack. The old football cliche of "Don't change a winning team" is pretty obvious nonsense as it ignores needed context, but the underlying notion of "If it ain't broke, don't fix it" applies in this case.
With or without Sanchez, City are favorites for the Premier League. With or without Sanchez, they are not going to be among the favorites for the Champions League. This would be a win-now move that wouldn't really move the needle on the winning part. It's doesn't fix the weaknesses City have at the base of midfield or the squad age problem and it's questionable how much this improves the attack. As an analyst, it would be fascinating to watch Sanchez and City adapt to each other; as a fan, I would prefer not to have to do so.