Gladiator

You can write this under any balance option – changing HP to something else.

Exactly. If you balance based on HP, ranged units and units with high attack (wolves, fairies, etc.) start to dominate. If you balance based on damage, then, on the contrary, tanky creatures (ogres, dendroids, etc.) become stronger.
And even if you achieve some kind of conditional balance (for example, it won't matter which castle you start with), other factors will start to play a role, such as artifacts, bonuses, magic, etc.

Added 5 minutes later
Ideally, the arena should be such that there is no situation where the victory of one of the players is predetermined at the start.