Drafting isn’t an official part of the game. Years of work went into making a game that specifically does not need drafting. Also, your opponent should never have any say whatsoever what YOU play in any competitive game. That goes against the point of having characters and letting people play the styles they enjoy or the characters they are good at.
If you play a casual game, it should be double blind character selection.
In a tournament, you’re expected to play the same deck the entire tournament. In a fighting game, you can switch if you lose and in Magic the Gathering you can sideboard in cards, but Codex already gives you an absurdly large “sideboard” every time you play. Much bigger than an MtG sideboard. Your three different specs (and 9 different common starts of heroX + specY) should give you enough versatility to deal with whatever. It’s definitely true that some combinations of heroX + specY counter others, and that’s intentional. Though you should have enough in your bag of tricks to deal with what’s thrown at you.
Logistically, it’s also very annoying to support people switching decks (multiple times possibly) during a tournament. So it’s best to not allow it, have the tournament run faster, and have it be more manageable to deal with potential cheaters (though that’s the least of the concerns here).