Oh, you were referring to Mystic Damsels! Sorry, I didn't get what you were suggesting.
The current Damsels all increase the speed at which a second round progresses. Heart Gem Rate would let you unlock the Shop upgrades faster. Reroll and Rarirty would let you waste less rolls on Lovers.
I agree with you there, these effects don't do much initially. The start takes just as long with Rate and Reroll until you unlock the Shop or Lovers respectively. The Rarity might make it take longer to unlock the Shop by spreading rolls more evenly, checking the math behind it would be difficult. In all cases these bonuses help reach the second Ascension faster, but initially their effect don't do much.
A Mystic Damsel that increases relationship gain would feel better than the current ones at the start after Ascension, and adding it wouldn't take much effort. But I still think the game needs improvements before reaching Ascension in the first place.