In proper 5e even those who don't care about their familiar in that way made a judgement call about whether the fight was worth risking 10 gold of incense, and being familiar-less until the next short rest. A situation which also means the more familiar-protective players weren't being entirely irrational, mechanically in their RP or personal choices. Personally I can't say I have been hyperprotective of my familiars, but I didn't allow my fey spirit animal pet to feel the pain of death lightly, and an enemy killing it was the surest way to bring whatever wrath my character was capable of.
In a system where every familiar gets 1 free death a day it's strictly mechanically handicapping yourself to not risk their life at least until they get their free death. Combine this with them receiving attack capacities and they feel a lot more like any other disposable summons.
And on the subject of the free death and them automatically coming back after an hour: This version has established they have hit dice which can, presumably, be used to heal duing a short rest (in 5e they all have a hit die as well, but the difference between damaged and dead is so negligible it is usually irrelevant). It should explicitly say whether the wounded familiar is using that extradimensional hour to take a short rest, or whether they can not do so, or else it should pick any other length of time for them to be absent.