Except that's just not true.
Yes, the season we signed Zlatan his form dropped significantly. But that was also the season he had serious personal issues when he broke up with his wife/girlfriend and mother of his child and she went very public with it, plus it was the first full season he was playing on the left. Both of those are more likely to have been impacting him rather than Zlatan being signed in itself.
When we signed Lukaku he spent the first half of that season as our best left winger. He literally started that season with 5 goals and 5 assists in the first 370 minutes (equivalent of 4 games) he played . Mourinho kept trying to drop him for Rashford purely because he liked Rashford more, but eventually even he had to admit that Martial was playing better and helping the team perform better so installed him as first choice. For a month or two then Martial was our simply best attacker.
At that point we signed Sanchez and forced him into the team by moving and dropping Martial, despite the fact Sanchez never got remotely close to how Martial was playing. Yes he was poor when he was played on the right, but he only got the chance to play about four games on the left again that season. He was poor in a couple of them but he was also good in a couple of them, but then got dropped straight away again so couldn't get a run despite Sanchez stinking up the place. The following season Mourinho was about to get fired and finally gave him a run of games again in desperation, and Martial (along with Pogba) dragged our team to victories and kept him in the job.
This season his form has obviously plummeted so I guess there's a chance it's related to Cavani, but I doubt it. I don't think any of the other three examples are a good testament to it. For me it's more likely he just started the season in very poor form and then unfortunately hasn't been mentally strong enough to dig himself out of it. Which is obviously a big problem in it's own right.