I think one of us is misremembering because Martial when he competed for the left with Rashford was the best Martial we had seen in years. He, Rashford and Lukaku meshed so well when either 2 or all 3 were on. People wanted one of them played on the right just to have all 3 on the pitch at the same time. In fact now that i recall, that one season competing with Rashford should kill this thing. Both players were that good against the competition of the other. That was maybe the last true meritous competition situation we've had since SAF left. The rest are manager favourite/preference situations. Even that was ruined by Jose stupidly signing Sanchez, so typical that he'd poison the one healthy competition with another unwarranted favourite.
I recall it differently. The competition seemed to spur each other on initially, but not for long. I recall on the occasions Martial got a start, him slumping off the pitch looking pissed off when inevitably subbed after 60 minutes. The calls for Rashford - Lukaku - Martial to all start together were due to frustrations with our RW options or lack thereof, and the lack of opportunities for our two most promising young forward options. Martial also voiced his desire to play as a 9, and Jose criticised his defensive work as a LW, called him immature and mentality weak, and requested the club sell him, identifying Sanchez and then Perisic to replace him. He was also not selected for most big games.
He got 4 league goals in Jose's first season. Better the next with 9, but not many important goals (scoring the 4th in a 4-0 victory etc). He was evidently better under LVG and during Ole's first full season. Stats alone, as you bring them up, he scored 11 league goals under LVG (from the wing, as a 19 year old) and 17 league goals in Ole's first full season). His best return by a mile. Its really not a debate.
In Jose's first season (or Zlatan's first season if you wish), Martial was very poor. Everybody points to that being due directly to having competition from Zlatan but ignore everything else. Jose changed his position (under LVG he was more of a striker or left forward), stripped him of his shirt number, was quite obvious in not really liking him, and his relationship with the mother of his child was breaking down (with her going very public about it). That's a lot going on for a 20 year old to handle. Maybe there might have been a bit more than just not being able to handle having to compete with Zlatan.
The following season when we bought Lukaku in, Martial outperformed Rashford comfortably on the left for the first few months of the season but Jose's dislike for him meant that he kept favouring Rashford. Finally even Jose had no choice but to acknowledge the form difference and installed Martial as first choice, with Tony going on to be our best attacker for the next two or so months. Then we bought Sanchez, moved Martial over to the right (where he has never performed well) and dropped him within a couple of games with him only getting the odd chance after that.
Basically if you go over his career seasons with us:
15/16: Good to very good
16/17: Poor, which people like to say was due to competing with Zlatan but as I noted above there was a lot more going on.
17/18: Our best performing left attacker when he actually got to play (and our best attacker fullstop in the only run he had as first choice), but through no real fault of his own he was 2nd or even 3rd choice for the manager most of the season.
18/19: Basically the same as above. Started out of the team, and Jose waited until he was about to be sacked before bringing him back in and he basically kept him in the job. Unfortunately was injured or ill most of the time under Ole.
19/20: Great, our best player over the course of the season.
20/21: Very poor, which people say was due to competition from Cavani. But Cavani was obviously considered second choice, and even while Martial was terrible Ole kept trying to start him over and over. So it wasn't really much of a competition.
21/22: Even worse than the previous season. Did struggle with injury quite a lot which wouldn't have helped, but even without that he was terrible.
22/23: Has started promisingly...
So I really don't buy the doesn't handle competition thing that some people go on about. His first bad patch coincided with a lot of stuff going on (most notably for us the change in how the manager wanted him to play), and the second happened when he was clearly 1st choice (and then continued the following season where it would have been more of a competition with Ronaldo). Meanwhile he was out-performing his competition in 17/18 and 18/19 when he got a chance.