XIV currently has 3 "pet" classes, 2 of which are from the same class. If we think about their concepts I'd say currently only SCH and MCH should have HP. MCH because for them it's no issue having to throw a turret back out if it goes down, SMN on the otherhand uses MP. As for SCH, their pet heals, so they need HP otherwise that would just be OP.
As for SMN though death to them means sacrificing a lot of MP to bring them back and even then when you get to the nitty gritty, what does a SMN's pet do that's interesting? Contagion is like the only ability that seems to do anything remotely interesting. So honestly, scrap SMN pets having HP and instead give them Aura's that effect the SMN in some way and these Aura would be the new Devotion effect.
Off top of head let's just say when you summon Titan, SMN gets dmg reduction, when Garuda is out, regen, when Ifrit is out DPS increase. When Devotion is used that AoE aura gives those following effects to all in range of the pet, so pet placement would become important for SMN, could treat it like a totem.
As for their "auto-attack" they no longer auto-attack, instead they all act like Summon bahamut, only acting when the SMN performs an action whether it be Ruin, Bio, Energy Drain, Fester etc under the same 1.5 second cooldown.
So pretty much you condense SMN pet actions to their Aura Trait, their auto-attack activated via SMN action and their Enkindle. Keep it that simple. When a pet is summoned it's treated as an effect on the SMN, they can instantly swap between pets but there is a 10 recast before being able to change pet again. Currently I'd say keep the Enkindle effects the same and maybe add a new effect to Dreadwyrm Trance that augments the Aura Trait when in said trance. Titan Trance could add dmg dealt -5% on target, Ifrit could add a DoT to target being attacked during Trance and Garuda let's say makes all Ruin spells instant cast. During Dreadwyrm Trance you wouldn't be able to change your pet, so you would need to decide beforehand which you want to use.
As for Bahamut Summon maybe keep it as is, but in all honesty I can see why SMN is a tricky beast to mess with. There is a severe lack of direction in the job, dots, pet, single target dmg, trance, summon bamaut, it just comes off as hard to syergize. I"d like to see what they do with it but honestly I do think when you compared them to the other pet jobs, they may have to remove the physical nature of the pets and just make them visible effects that add to their dmg rather than target-able creatures.