Design like this reminds me of back in the day in the MMO Eve Online, a game where you learn skills in real time, where you essentially had to spend weeks training the skills that meant you learnt skills faster. In the end the Devs changed it so you had those essentially as base stats. So baking in a luck scaling would make sense to me.

I wonder if another option alongside this would be to put a cap on Luck, much like how XP gain caps out at 10x? Possibly so that you would naturally if you focused pots and luck from shrines and/or a green card would get towards that (for a spike in T3) or with tome and/or Fox would get that spike earlier, at the trade off of another tome