So, who wants to setup a "balance" tournament: an obnoxiously long series where top-ranking players need to play a TON of games against each-other as every faction (and combination), solely for the purpose of getting win:loss statistics? I'd suggest a similar format WCS, except each player matchup needs to consist of a "best of 5" of every faction combination (5x USF vs. Ost, 5x USF vs OKW, 5x etc....).
Really though, considering the player base of CoH2, getting a complete statistical breakdown of balance that's as accurate as it needs to be is very unlikely. If the game had daily concurrent player peaks over 100k it would be possible, since top-level play would actually consist of only top players. Unfortunately, even with the free give-away a little while ago, its only reached 22k peak concurrent players, and that average is now down to around 7k (based on steamcharts).
Even so, I still think the WCS is a better source of balance data than Automatch. Players in the WCS were all in the top 150 for 1v1, whereas in automatch it's not uncommon for top 100 players to be matched against top 300-500 players, since that's the closest available.