A lot of the discussion of Martial's game and Mourinho's use of him seems to look past a basic point: Mourinho simply refuses to start Martial and Rashford on the wings together in the 4-2-3-1 or 4-1-4-1 formations. Why? I'm not sure, but probably because he thinks they are too similar, both essentially wide forwards that don't contribute a lot defensively and aren't suited (like Mata or Mkhi) for dropping deeper and helping with the buildup. This isn't a crazy quirk of Mourinho. Lots of managers who play these formations prefer to have an offensive oriented wide forward on one side and on the other side either a runner or a wide playmaker. Wenger will not start Alexis and Walcott on the two wings together either.
The basic reality for Martial last year was that he only got a chance to start when either Ibra or Rashford was unavailable or, for the latter, not selected due to form. I think it will be the same for him this year, but now with Lukaku at CF instead of Ibra. Its not Perisic that will hurt Martial's playing time, because Perisic would be playing a different role, as the hard charging and defensibly responsible winger that balances the more offensive wide forward. The issue is Rashford. Assuming Lukaku is an automatic selection at CF in most matches, Martial will have to beat out Rashford to make the starting XI. And this will be hard, because Mourinho clearly really rates Rashford.