There are at least two big reasons for mirror matches aside from "would be interesting" and "its about the maps."
The first reason is making best of 3/5/whatever tournaments much easier to run: in CoH when you play an odd number of games, one person only gets to play their preferred team once in the best of 3 or twice in the best of 5. You can do things like "whoever has the most VPs total going into the third game chooses their side" or something like that but that's an annoying consideration for players to deal with and
especially when one side is better for the map they're playing in the last round or better because of Relic's latest patch, it sucks to be stuck with the side you don't want. Mirror matches allow competitive players in tournaments to play the side they want to play in each map, or even just in the final odd matchup (you could still have the first matches be Axis vs. Allies if you really wanted).
The second reason mirror matches are important for competitive play is that they let people get really good, like REALLY good, at the game, in less time. This opens up the competitive scene and lets a lot more players in - it lets in people who don't have enough time to become master class with both teams but who do have enough time to pick one team and learn it well. Let me quote Sepha from the second page:
While I can say the same for a lot of the competitive players I know who left on day1 of CoH being released because their were no mirror matchups, I can't say that the amount of people in that group is larger than people who don't want mirror matchups.
There's a big group of competitive players who will never touch CoH 2, never play in tournaments, never keep the game alive for months and years after release, unless there are mirror matchups.
Now if your favorite part of Company of Heroes is pretending like you're watching World War 2 combat footage you won't care, but if you want exciting matches for years to come, and if you want a healthy, thriving competitive community that makes tournaments exciting and closely matched, then you should want mirror matches.