So get this; having Bastian out will sometimes make you able to loot a slightly less trashy trash pot. There are three versions of this slightly less trashy trash pot and they all take up in total 3 additional slots in your inventory.
But since the drop is so rare, and only a very minor upgrade from regular trash pots, it's unlikely that anyone will ever use these for any real purpose. Regular trash pots drop in abundance - and can be quite useful for example in healing veteran dungeons depending on your group. You can easily gain full 100 item stacks of them, and they can regularly be bought cheap off guild traders.
Bastian's trash pots however have negligible benefits over regular trash pots, but also will take you probably months upon months of playing to reach full 100 item stacks of because their drop rate is super low for some reason.
So, with these three points in mind; negligible benefits over regular trash pots, having to micromanage an additional 3 inventory slots, as well as possibly taking months of playtime to reach a full 100 item stack; why would anyone want to complete Bastian's achievements?
The keepsake you get from completing them, makes it so that this "perk" is active at all times in every part of your playthrough f.o.r.e.v.e.r, even when Bastian is not at one's side.
Can we either get an option to turn specific keepsakes off, or a full rework of Bastian's perk? The only thing I need to complete his achievements is bringing him out when in Eyvea, and I keep putting it off because the idea of being bogged down with it in my playtime is offputting.