I had already thought about it and I think it would be cool, maybe bonkers and others would finally want to make an account
A few other games like this, such as Rocket Golf, already have a fewest shots category and as cool as the idea is I personally don't feel the need to add a score category. I can't say and don't know what Ox's opinion on this is, but I'm not willing to create and maintain that. That doesn't mean that new mods are out of the question if such a thing were to be made and enough activity warranted it.
Agreed, I'm not interested in tracking that on a speedrun leaderboard. You can start a Climb Higher Discord and start tracking it that way if it interests you. Also, they already track this (I believe) in the developer's discord, to an extent.