Eh, needless to say, I almost fully agree with
Matalarata here in that balancing a SP focused game for MP foremost harms the game.
So, I won't go over all those arguments again, he does a good job at that.
I would even go one step further and say that MP itself would be way more interesting if factions and strategies would not only be more asymmetrical but also more varied in sheer power and more RPS like in not only units but races themselves.
Imagine a game with, say 10-15 races (yes, that's a lot) and each of them plays between "somewhat" and "very" differently and also mix in RPG by having a main hero unit.
It was fully balanced for being interesting to play in single player mode, but also offers an exhaustive multiplayer mode with persistent MP worlds (co-op and/or vs campaigns, imagine Emperor: Battle For Dune or WBC3 campaign online), matchmaking, leagues, etc. you name it.
Now, one of these races (race A) can be considered the overall best, without an argument.
However, another race (race B), which can be considered one of the worst otherwise, has a much easier time against it due to the build flow and what units it has available.
Additionally, the hero unit is permanent and consistent between matches/across a campaign and as you level it up you can invest in skills improving its combat prowess or skills improving the race as a whole (again, similar to WBC3).
Just like some units are by nature stronger against some others, some of these races are by nature stronger against some others. But each race has weaknesses that at least one race has a strength against.
In single player, this means that each player can set their own challenge by choosing a race, while figuring out strengths and weaknesses of each race AND the overall strength of a faction is an exploration aspect of its own - somewhat similar to Dominions, I'd say.
You can also experiment a lot with your hero/race synergy.
Single-player wise, this would be a dream game (to me, at least). And if it didn't have multiplayer, I'd be fine as well.
But let's say it has MP.
Multiplayer wise, I can already hear "everyone will play race A with hero X because that is strongest".
And if you'd do matchmaking, scoring, etc. like a normal RTS game, I'd agree. Or rather, I'd say that people would still pick whatever race they like most, but complain about it being shit tier, unable to gain ground in leagues, etc. and would stop playing MP.
But let's not do that!
Instead, for scoring and league positioning etc., each faction (and if you want to get extra thorough, each faction/hero combo) gets assigned a score factor against each other faction. This score factor determines your final score after a match, as a multiplicator maybe.
For example, race A has generally the lowest score factor (as it is the strongest), but a higher one if playing against race B.
It will simply be extremely hard to gain a top position league-wise if all you do is play race A - not only number of wins count, the score does, most of all.
Playing race B as your main will be tough, but even gaining as much as a "valiant defeat" against a stronger race to play against will grant you a score that is as good as a victory, winning will actually be extra worthwhile.
Now, balancing how this score is calculated wouldn't be easy, but I'm fairly sure it can be done. Analyzing statistics in beta would help a lot here.
The important thing is that now, not everything is about winning, it is about getting a good score.
And the best thing? Devs could stop reaching for a perfect balance that cannot be achieved anyway, and instead go for way more interesting things to pursue.
None of this means that there can be no balancing done. Of course, it can - if something is too extremely strong or weak, that can be adjusted. A shitty player shouldn't be able to beat a good player, no matter the faction combo, that would be where I draw my "balancing line".
But as soon as you end up trying to make every race work equally well against every other race, you invariably end up making all of them less varied and interesting, too.
I think that could be a very worthwhile experiment to show/test that even in MP, typical competitive balancing isn't necessary.