Ive still yet to have that happen. Must be due to me usually having the AI set to focused attack. Even on the default though they dont seem to. Since I usually run with 2 other healers its odd that it has yet to happen
I've had it happen to me quite often on the standard command. I'm not sure if it varies from character, wouldn't make sense to give different characters of the same class different priorities, but it feels like some characters are more likely to do certain things. Beatrice is very quick to revive and heal, more so than matthias. She often rushes to revive me when I'm not too far away. Beatrice <3. Nobody will revive your accessory though </3.
As for Nina, because she's using a small sword, she likes jumping onto abductors and cutting things off. She even rescued my accessory from the Tiger with 5 Seconds left on the clock while I lay dead on the floor, after some sort of odd double dragdown/ko. It's times like this that you appreciate the PS4's share function.
I'm having a lot of fun. I'm at code 6 now with 22.5 hours clocked and 942,000 years on my sentence. I don't find the game unfairly tough. It's a busy game since there are a lot of enemies that shoot at you. I like to do shingeki type rushes on human enemies and snipers. I find it the easiest way to hunt them down when they're running around. Either running + attack to do a quick wide area forward slash or lock-on, ibara + triangle, immediately ibara again for a return slash, repeat until dead. You can even press triangle to slash even though your ibara isn't on the enemy, so long as you're flying in their general direction. It uses up your ibara gauge quickly but that's what the recharge points are for.
I've had an easier time ever since they introduced boosters and we get to up our defense a bit. The healers use their first and second charge ibara quite often but I don't think I've ever seen the defense support (??) characters use theirs? I've also not seen the first charge of the attack ibara used, only the second.
And yes, keep your accessory and healers close. I tried letting my team take the spider while I distracted the Tiger to disastrous results in the special mission. I kept dying with no one to revive me and used up my 5 respawn chances, resulting in a loss. Nobody told me special volunteers are a one chance only thing! How often do they appear?