Removing the short rest restriction on Find Familiar will likely give a lot more usage to the spell. Summoning something like a rat or crab that will simply die when its highly intelligent AI walks it onto a fire surface does nothing to incentivize summoning it in the first place.
My two cents concerning familiars is roll it back to 3.5e, or PF - summoning a familiar creates a non-combat creature that gives a small passive bonus to the caster. Raven familiar gives +1 to Perception checks, rat give +1 to CON saves, stuff like that.
At present, summoning a <=10 HP creature with stats equating to a level 1-2 combatant has far too niche of an application to hog a prep slot and be restricted to one per short rest.
