Foden & Sanchez are kids who have their whole careers ahead of them, however we need these reinforcements now. Think about the Wolves match. We weren't able to even do what Arsenal did and change all 11 players and retain some level of competitiveness. We've always sought to have 2 teams and be able to rotate and cover without an appreciable drop in performance and adding the likes of Sanchez moves us toward that.
You talk about Sanchez's lack of pace, but have you considered that Gundogan, KDB, D Silva, B Silva, Fernandinho & Toure aren't exactly like shit of a hot shovel in the speed stakes? Sanchez has never been known as a speed merchant and I saw enough yesterday to suggest he has more than enough speed to fit in at City. Sanchez only has 1 goal this season which is fact. However, how many goals do Gundogan, KDB, D Silva, B Silva, Fernandinho & Toure have in a team who have smashed all kinds of records this season so far? By your metric, we should be looking to ship them out because of their lack of goals.
Talking about Sanchez effectiveness in the final third. Have you considered his wanting to move is because he's realised that even at his best he can't elevate Arsenal above fighting for 4th most seasons? Messi is probably the best player there's ever been, but if he was to move to WBA or WHU, would that make them title contenders? One player can make a significant difference, but NOT when you have teams of the strength we have in the Premier League.
Finally, I trust Pep's judgement. Yesterday I imagined Sanchez playing for City and I'm happy to say I was more than happy with what I saw just as City, Arsenal, Juve, PSG & Bayern must. Just because some fans can't see this or share this vision, doesn't make Sanchez to City a Rodney Marsh style error in the making.