Absolutely it can be competitive. Just about how you coach them to play. There's so many variations of a 4-4-2 that's still a 4-4-2 that it'd be fine, just like how Sir Alex used it. No reason that wouldn't work now. One of the strikers is more of a 10, one side the winger is more advanced with a more reserved full back, the other side the winger is more a wide midfielder and more reserved while the wing back can push up a bit more to provide extra width, and so on. Also I never felt like a good 4-4-2 had 2 box to box midfielders. You don't want your midfield running around everywhere and not having positional discipline, that's why Gerrard and Lampard never worked. You want midfielders who were well rounded, but primarily can control the tempo of games and are smart positionally, know where to cover space and how to cover it. That's why Sir Alex's midfields were always so good. Off the ball, tons of teams defend in a 4-4-2 anyway so that isn't anything different.
Just at United with who we have right now I'd like to see this used with our current injuries:
Zirkzee
Bruno
Garnacho - Ugarte - Eriksen - Dalot
Dorgu - Yoro - De Ligt - Mazraoui
Onana
Unfortunately the only winger for either side is Garnacho, but Dalot would be a wide midfielder (not a wing back) and Mazraoui a normal full back, while Garnacho would have more attacking freedom. Bruno a pure second striker, Eriksen and Ugarte in midfield to control games (obviously Eriksen's lack of legs an issue here, while Mainoo's lack of passing range is an issue there)... but I think it'd be decently balanced. Tons of players you could pick from. Zirkzee up top because I can't stand Hojlund and don't think he'd work for anything, but if we signed a CF can use Zirkzee as the partner and move Bruno next to Ugarte in midfield. Also would need another wide player (put Garna on the right to rotate with Amad as the more attacking one, and then a more balanced left footed left wide midfielder to provide width and balance on that side). The key is to not have both wingers/wide players be super attacking guys. Sir Alex didn't use Ronaldo and Nani together often at all, he would always balance it with Giggs who helped a lot with controlling games and being an extra guy inside too. Same as when Beckham used to be there and Giggs was more of a flying winger.
If I'm looking for signings to transform us into a 4-4-2/4-4-1-1 that could work right now, I'd aim for having a main and 2nd 11 like this:
Osimhen
Cunha
Garnacho Ugarte Bruno Amad
Dorgu Yoro De Ligt Mazraoui
Onana
Hojlund
Zirkzee
Quenda Collyer Mainoo Mount?
Shaw? Martinez Maguire Dalot
Altay
So signing Osimhen, Cunha and Quenda. Ideally a backup/rotation for Ugarte would also come in, and then another wide midfielder. But takes our current 2 "strikers" and makes them both bench options which is better for them.