On your point about it being a great swap, that's of course subjective but I think you could have spent £150-180m better than on Sanchez for a couple of years.
You are looking it in isolation though, rather than the bigger picture
It certainly doesn't hurt bringing in a world class player (admittedly when he is in the mood to be) to attract other similar calibre players over the next year or two
You also have to consider who is available right now to hopefully help Utd over the finish line of the top four this season, the only player Ive seen us linked to is Lucas Moura from PSG who would be a gamble to say the least.
Liverpool have already strengthened considerably in Jan (which may well turn a few of those draws into wins by shoring up the defence), Chelsea is debatable whether they have really strengthened or not, but do they need to - Arsenal certainly have a more motivated player than they had before but debatable whether they actually have strengthened yet - and of course this is with 10 days to go of the window being open - who knows what Spurs are upto.
I think its fair to say that Utd have a much better chance of a convincing end to the season as well as a much more enticing project going forward (to attract players in future windows) once Sanchez arrives.
Unquestionably an insane amount of money - even if it still may prove to be wildly inaccurate - its debatable how much less you would pay on a free for a similar player. In one sense the fact Mkhi is included in the deal as you said works for Utd, as we are getting rid of a player that didn't really work the way JM wanted - Mkhi's contract was probably worth ~ £15m with the time remaining maybe less).
With all the add ons etc excluding wages - because its impossible to know who to believe right now - even if Utd are paying a total of £20m extra in signing on / agents fees etc etc than City , its still a lot of money but really will it make a vast difference to Utd's profitability....highly unlikely. Champions League is king, especially now that tv money for getting there is worth so much its really a small price to pay.
edit: As I said initially, the upside for Utd is the certainty around the deal. They don't have to wait, possibly until the summer, for somebody to come in for him and negotiate a deal but you can bet your life if anybody from Everton to Wolfsburg came in for him, Utd would be demanding £30m or so given the fees that others have gone for.
The only thing I would say to selling abroad is that without doubt we would have to give Mkhi a pay off to cover wages etc moving to Wolfsburg or where ever, from what Ive seen so far going to Arsenal this isn't the case.
I haven't seen this being the case here anyway - if it is already then fair enough