I keep everything I pick up - because at this point I’m sure I’ll need it later! But yes, given the restrictions of their inventory system, the ever-growing amount of crafting ingredients needed for different levels of recipe is quite frustrating.

The only other game I’ve played with such a complex crafting system was the Atelier Iris series, and from memory their inventory was a dedicated item list of all the materials you could possibly obtain in the game. It also allowed for substitution of different items in the same class, which would affect item quality - so you could use any sort of leather in your blacksmithing recipe, or get a quality boost by using nicer cooking ingredients. (It was more “insert ingredients, get result” without the crafting, and the challenge was on quality ingredients and discovering new recipes by substituting critical materials. I preferred it to this game, I think.)