You really would need some advanced statistics math here, given how factions are not played equally, or facing equal match-ups.
We do have match-up specific stats as well, but elo distribution alone without normalizing faction pick difference won't do any good.
In my mind I was mostly thinking about 1v1 where at least the combinatory issue does not exist, although it technically shouldn't matter.
I am not sure how complicated the analysis would actually need to be. Maybe just looking at ELO distribution within teams should already give some info. Weak factions/team combinations would have a consistently lower ELO across the board. In case something is "easy to get into but hard to master", ELO range might be compressed more than other factions. This would not resolve factors like e.g. "double USF is good against double Wehr, but bad against double DAK". This could maybe be done by filtering for these special game setups (with all the caveats of Relic not directly introducing a ladder for that), although I yet don't know if it works out and how exactly it would look like.