Indeed perceived balance is an important thing to look at. Nice input also, which i want to repeat and then add a little. First, the skill, or experience gap between players involved. The quoted posts below very nicely elaborate on that.
Based on a year of experience with random teamgame matching, the expanded search is purely onesided, ie. if an axis team has been waiting for a long time and has thus expanded their search to a humongous range, if any two players join the allies queue, they can get instantly matched to the axis players no matter how large the ELO differences are. So with the current generally 100% axis searching pattern, you get absolutely horrible matchmaking as allies which leads to even less players wanting to play allies.
There's also the issue of the system not differentiating between randoms and arranged teams, leading to even poorer matches. But this applies to both factions.
...The Solution would be to either, make Allies cooler, or change the Matchmaking algorithm, so that no matter how long you wait, you wont get paired with players way worse than you.
The negative effect of this would be, that Axis waittimes would be increased even more, but in the end the problem is here right now already. With the changes, you will need ages to find a balanced game, now you need ages to find a balanced game. But the added positive would be that maybe some more people would play Allies.
Another thing to factor in is the amount of coordination the favored gameplay needs. With randomly matched teams and the casual playerbase in general, to succeed in doing what the factions are proposed to do by the meta, allied play is more demanding in terms of coordination. With axis the objectives are pretty clear, the herd does the rest. With allies you have to keep the momentum, flank around, play as a team, use all directions for attacking.
Antoher perception deceiver is the scaling of players involved (2v2->3v3->4v4), withoug scaling the maps they are played on respectivly. Faction Design is made for a certain dynamic between factions and the possibilty of success is determined by the possibilty to follow the laid path. Maps are in relation very small, im certain map size is another reason allies feel less balanced; or are much harder in bigmodes.
How to solve those? Jumping into a game as allies for a quick joy, beeing matched horribly getting owned within 10 Minutes, dragging the game for another 15. Or on the other side going into rotation getting randomly matched, with most games ending in a decicive but not very fun victory. Since it indeed spoils enjoyment for a lot of players it is somehting to be solved, after all we love the game, right?
1.
Lichtbringer pretty much named the most obvious solution to what cruzz described. So, hardcap the allowed skill difference. Or incorporate a way to decide. Maybe an ample system with the possibility to confirm beeing matched against a team with much better elo rating.
2.
Improve random game mode. Make it search teams, possibly with amples. Confirm and go for the hunt. Still gives the possibilty to join teamgames when no one you know is arround, and increasing the Team aspect by featuring it hard. Allies need to coordinate. Out of 4 games i joined in 2 people dont communicate at all, ignore freindly hellos and questions about strategies. Beeing forced to start a game just to realize your teammates are defmute and dont know the hotkey for retreat is a bummer which would be avoided.
3.
Maps. Make. Them. Bigger. Im not sure if the amount of points in general should go up, or space alone would do. I'd love it if there would be a supersized map of one of the more problematic 4vs4 maps to check it out in practice.