In an attacking sense, there were few better on the left than Baines in the Premier League last season. Defensively, there are questions, as there are with most full-backs, but teams tend to provide an answer for that anyway. It seems to matter less nowadays: you'll have your wingers tracking back or, as United did with Marouane Fellaini last night, the central midfielder. So while a lot of television analysis and pub talk is devoted to a team's vulnerabilities out wide, it isn't as much an issue as it used to be. It's a pretty effective way to carry the ball forward, especially if you're Manchester United. (You've only got to look at how great Rafael was in 2012/13, his most successful campaign yet.)
Evra has always been an attacking threat, but there seems to be something slightly different with Moyes' Evra to Ferguson's. There are a variety of reasons to not play Ashley Young -- how long do you have? -- and him preventing Evra from being as good as he can be going forward is one of them. Young, unlike some of the other attacking players the team has, is fairly limited. He can play on the flanks, but that's it. With Danny Welbeck, Shinji Kagawa, Wayne Rooney and perhaps even Robin van Persie, United have players that can run around and assume all sorts of positions. Evra, then, has all the freedom he can ask for down that left-hand side. He's quick and intelligent, and may well be United's best crosser of the ball after Van Persie.
This is not to forget that Antonio Valencia exists. He definitely still does, as many found out on Tuesday. He does have a fixed position, but no bother. The right, unlike the left, has not been a testing ground for new ideas. That's been the one constant this season. Where the Community Shield game had Welbeck and Ryan Giggs chasing balls on the left-hand side, but neither really playing there, the right had a traditional winger in Wilfried Zaha. Valencia then took over for Zaha and hasn't been made to budge since, while the left continues to undergo an experiment. This imbalance also happened against Swansea, then Chelsea, and now Leverkusen. The two exceptions were Liverpool and Crystal Palace, where Young played. That's four games to two.
This can be explained: in May, Jim Fleeting, Scotland's Director of Football Development, spoke of how Moyes noticed that "everything was going through the middle area of the park." It would, yes, be foolish to abandon wide play altogether, so that's not what United are doing. They'll find a compromise. Give Evra the license to run and have others help him out, but also look to do things in the middle. It suits Welbeck and Kagawa, two players that people insist should play centrally, but who might struggle to get games with only so many positions to fill. It works for Moyes that they're chosen ahead of a Young or a Nani, rather than a Rooney. This is also good news for fans of Adnan Januzaj -- he's an attacking midfielder that can play on the left. Giggs, meanwhile, does not have the legs to be a wide player for 90 minutes, but still has some of the qualities to be one for half that time, while also controlling the game from the centre.
(What made the 2007/08 team so good was how nobody upfield really had a fixed position. Cristiano Ronaldo, Carlos Tevez and Rooney could do whatever they wanted. Now, look, the current squad have a lot of work to do to even get to that level, but playing someone like Kagawa and leaving Young on the bench is a fairly promising start.)
It's also worth noting some of Evra's good play so far as a result of all this: the first goal against Bayer Leverkusen should not have counted, but the cross for Rooney was perfect regardless. In Moyes' first game at Wembley, he set up Van Persie for his first from a(n absolutely) vacant left-hand side (see gif). The following week, he did something similar at Swansea: an early cross, hit like an indirect free-kick, that the Dutchman could not convert.
At Everton, Moyes relied heavily on Baines. There were some statistics (which you can google) that many read as being proof of Baines' status as one of Europe's best, but however much we should treat stats in relation to talent, what the big numbers definitely tell us is that he's involved a lot. This might be why Moyes wanted Baines so much -- the added responsibility afforded to Evra could instead be Baines', a player he knows, with a whole flank to himself.
While the Scot was disappointed not to get his man in the summer window, presuming Evra continues his good form, he should be able to get over it pretty quickly.