While you are well articulated, I just don't agree. There is a mountain of evidence of why signing players that doesn't have momentum most often is a bad choice. Balotelli, Torres, Sanchez, Falcao, not gonna list a 100 players though. My point being is that there's more evidence of this than evidence that the opposite is true, hence you can make this overall assumption as the sample-size is not just 1-2 United players. How many players can you think of that had a 1-2 year old slump and came back to their great standards? I can't think of many. At least not as many as the opposite way.
Hence is why I was annoyed about your response. I didn't just drag a conclusion out of my arse based on one Sanchez signing. There's so many cases of this that the sample-size should be note-worthy, and Fergie's reign maybe showcases this the best, as he had great succes (great motivator, yes) but always bought up and coming big talents and never the other way around. But yes, in general you cannot draw a final conclusion about anything. That much is clear. You can however make some pretty good assumptions and create criterias for what is the best signings risk-wise. Signing a player who's not hitting it, is a risk. An unnecessary risk imo, as you have to find the odd one out that does become great again.