I quite like Mata on the right compared to Mata in the middle, though there will be games (perhaps in Europe) when he gets a chance centrally. He might have great dribbling and retention skills, but he's a little chap with barely any muscle on him, and I can't see him coping with the hustle and bustle in the middle of the park. Nearly every team in the Prem plays a holding midfielder or two nowadays, and they're no shrinking violets usually. I don't think it's a coincidence that we saw probably our most muscular attacker playing there yesterday.
I'm guessing here, but I assume Van Gaal wants Mata to stay relatively deep so he can come inside and play those penetrating passes. The only problem with that is if there is no-one pushing the defence back, then there's barely any space for him to play in, and he can be neutralised fairly easily. Unfortunately, Rooney doesn't really look to go beyond the defensive line, nor does Young, and Depay was a little deeper than I expected him to be (when we had the ball). Darmian was impeccable defensively, but he is defender-first and doesn't do any Dani Alves runs in behind.
On the other side, Young plays higher up, but he possibly has even fewer options than Mata. We don't have Fellaini pushing up into the box now, and as we all know, the backpost cross to Mata is pointless because of his height, and more importantly, he plays deeper. There was a good example of the problems this can cause yesterday - Rooney had the ball in the middle of the Spurs half and it was 3v4 or something similar, and he had to wait for Mata to come and join the attack. By then, the Spurs midfield and full backs had got back to help out.
As I said, I think this is deliberate by Van Gaal to provide us with assymmetry and a bit of unpredictability, but for it to work, we need at least one of the following:
1. A striker who likes to run behind the defence and through the channels;
2. A winger that breaks his back to make a run from out to in, and can receive the ball behind the defence and finish ruthlessly
3. A right back that effectively swaps positions with Mata and pushes the left side of the opposition defence back.
Since we have a very attacking full-back in Shaw on the other side, it makes sense for Darmian to be a bit more defensive-minded, so 3 is out. Rooney appears to be indispensable, so 1 is as well.
It seems then that 2 is the answer, and Pedro is that winger. He seems the perfect solution, and I don't think Van Gaal will be massively bothered about losing Di Maria, who is a player who prefers to cut inside early rather than linger for the through ball in behind.
A lot of posters on this forum have complained that Pedro is just a good finisher, not a chance creator, but I think that's probably what makes him so attractive. He can stretch the defence wide and force them to decide between playing a high line and risking being punished by his pace, or playing a deep line and giving the likes of Mata room to play. We don't have anyone with real frightening pace at the moment, and I think that is what Van Gaal was on about in that interview when he talked about needing a top attacker to open up defences - Young, for example, is fast but he doesn't make you worry about him getting in behind you, since he's not particularly ruthless in the finish, as we saw a couple of times this pre-season (there was a prime example against Barca) and yesterday.
TL;DR: imo, Van Gaal wants Mata on the right to give him space to come inside and play. Problem is the lack of an "opposite" on the other side who can run behind.