Maybe categories of starfish, cocobo, delevel, block would be useful ?
combat - anything which does damage to your opponent in combat as its main (or only) effect
delevel - anything which can delevel the opponent during combat
block - anything which can block an opponent during combat
whelp - anything which restores both HP and MP during or after combat
starfish - anything which does damage and restores MP mid-combat.
coco
abo - anything which gives you Meat mid-combat. (note that a Cocoabo is also delevel and starfish)
A lot of those will pull things from the "other" list, rather than the "combat" list.
A question is, how do you decide to omit something from the "combat" list if it really does do damage?
The Elemental fairies could be solely item drop - but they do do damage.
Starfish-type familiars do damage and convert it MP, so omit them.
What about the nemesis familiars that effectively add a category if they happen to have equipment?
I'm all for this change, but it will take effort to categorize familiars usefully while dramatically shrinking the pure "combat" familiars without hiding the fact that the ones you removed do damage in combat as a secondary effect. If that's important.