On second thought, I think I know why this isn't included from the beginning -> this system has the potential to be abused for essentially cheap wins.
Imagine the following scenario:
You see a heavily armored enemy fighter slowly walking up to the bridge. There doesn't look to be any supporting characters in sight. With your team in perfect defensive position you click end turn.
The next turn, the fighter pulls out a dagger, cloak & daggers into your midst, vaults over the head of your wizard, disappears into thin air and cuts him to pieces with a mortal blow. Oh, adrenaline! Backstabs X N, your ranger is down. *Poof* he uses tactical retreat and enters sneaking mode. Turns out it's actually a scoundrel/huntsman hybrid with glasscannon, warlord and backstabber. The sword & armor is just for show. You concede the match. GG.
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I think it's fair to say that if we want to add custom characters there should be some ways for all players to check out each other's character builds thoroughly before the match starts. At least if we want to keep things competitive instead of having all the first matches degenerate into people face checking unknown random things disguised as all kinds of stuff.
To me, that is true strategy. Where is the strategy when you can just look under your enemies hood? I say good on the player that fooled the other player. They used their brain to out-smart the other player. Allowing players to disguise themselves, would just force you to keep that in mind when making your fighter.