Barca dominated with technically one of the greatest teams of all time. They were able to do this because they could play in tight spaces and retain possession extremely well so they could shift the opposition about much more easily and create space. Imagine passing the ball to Lukaku and watching him do a Messi by evading multiple tackles and passing to another attacker in space...
Also Fergie United dominated but we always played with a lot of width and proper wingers, even when we had Ronaldo we always played a proper winger on the other side. The whole mantra of the Fergie team was to play very wide and deep to create lots of space inbetween the lines and then use movement and quick passing/decisions to exploit that space. We had attacking fullbacks but that was never in lieu of wide wingers.
The reason Martial and Rashford didn't play wide is because they aren't wingers... What would they do if they took the ball to the byline on their left foot? They aren't going to cross it are they? They'd just turn around and pass or square up to the defender and try to take them on. Actually good evidence of this is the Barca game pre-season, when Rashford played on the right we actually did have very good width because he was able to take the defender on the outside and that gave us a lot of space in the pockets in the middle of the pitch. Rashford never does that on the left because he isn't good with his left foot. Now take this example from a pre-season game of Perisic (skip to 1:58) to see exactly what I'm talking about. This is what he could bring that we don't have right now on the left side, if you've got guys who can do that then teams can't defend deep and narrow because they'll just get exploited by the crosses on the outside
While I agree Dembele and Lemar are better players, they are very unrealistic signings. Why would Dembele come to us when he's got offers from Barcelona? Never mind that Dortmund don't want to sell him anyway. Likewise Monaco are adamant not to sell Lemar and he too has offers from a number of top teams. Yes they are good but right now we aren't even being linked with them and there's no indication whatsoever that we could get them as an alternative to Perisic, both would be incredibly difficult deals to pull off.
The issue is you aren't seeing the bigger picture of the tactical importance of a wide winger on the left side. It's not that Perisic himself will score or assist 15/20 goals. It's that he will bring another element to our attack that can cause new problems and issues for the opposition defence. Last season our team was only threatening through the middle, no one was doing anything productive out wide expect possibly Valencia, but even he rarely put in a good cross which we could score from. If we add another element to our attack, someone dangerous from wide on the outside and who can put dangerous deliveries in, it's not just an option to score from those crosses but also to force the defenders into pulling out wide and making them think about new and different problems. This all helps to unsettle the defence and make the middle less congested or rigid and allow our central players more space and opportunity in dangerous areas to score or create chances.
Any team who attacks very 1 dimensionally is going to be easy to defend against. If a team played only long balls against us, we'd play Fellaini and our tall centre backs and just defend in the box and easily snuff out their approach. However if that team also had tricky wingers who could beat a man and dribble into the box that's now a new element and we'd have to be wary of that. That would allow possibly their fullbacks time and space to put in good deliveries and hence use their aerial ability more effectively. It's a simple example but I'm trying to paint a picture of how the bigger tactical picture works, this is how we need to think about the Perisic signing as that's where the big influence will be.
That Fulham game was just a joke... The reason we put in so many crosses is because we had 0 plan or tactics of how to break teams down so we just got the ball in the only part of the pitch where there is space (on the wings) and just crossed because that's all we could do. There was no plan and that's totally different to the situation we're in now