Extending some "party member" effects to pets...

[Yinnyth]

I think they're afraid of the deevaluation of "Pet: " gear, the overpowerness of stacking buffs plus such gear etc.

I think they're afraid of making any "Pet: " gear that's actually useful. The best pet gear in the game is perpetuation cost gear for SMNs because enough of it gives them a free pet. The rest of the pet gear is marginal at best, and certainly nothing compared to what DD jobs are capable of wearing on themselves. The fear of a pet becoming overpowered with buffs is as irrational as the fear of a level 99 SAM wearing level 40 gear becoming overpowered with buffs.

First you're comparing the pet to a SAM or WAR. Yes I concur the pet alone won't do as much as them, but pet + master might as well.

I can't speak for BST since I haven't played it since I capped all my SJs way back in the day, but PUP is in no danger of outdoing heavy DDs even if you factor in the damage from the master and the puppet. This is mostly due to how overpowered haste effects are, especially when combined with double, triple, and quadruple attack. Pets will not reach capped haste. Maybe with soul voiced marches and 3 overdrived wind maneuvers, the puppet could hit that 80% cap, but they'd still have several disadvantages:

1. No empy/relic/mythic frame for puppets to increase their base damage, so their base damage is determined by their level and no amount of gear grinding can change this.

2. Very few pieces of attack gear available for pets, so the pet relies completely on maneuvers and buffs for its attack. The maneuvers still fall short of giving the puppet as much attack as a standard 2h DD with berserk and average gear, but the DD still gets buffs and the puppet doesn't.

3. No food for pets. Only the master can get boosted by food, and that's mostly a waste because (if gear and buffs are ignored) the puppet is stronger than the master.

BST can bring reward time to very low recast times, and the highest tier of food with a good build (and Beast healer) heals for like 2500 instant plus a fuckton of regen.
And let's not forget Dawn Mulsulms.

Which is supposed to be the equivilant of meds which players use. Granted, meds currently suck because they don't stack well enough, their use timer is too long, and medicated status is BS for most of them, but if you want to spend gil to improve your survivability, or the survivability of your pets, you should be able to. Once they get around to fixing alchemy, this will be a non-issue because players will have even stronger potions than pet food, automaton oil, and dawn mulsums.

Also to my own view the main concern SE has before allowing buffs to be applied to pets it's not the fact that they would do too much damage, because that wouldn't really be a huge issue in the end.
I think they're afraid about the fact that a small amount of people (or even a single player) would be able to circumvein their precious battle strategies by deploying pet jobs against NMs.
This already happens to a certain extent, and it annoys a lot of players already, just imagine the scale this would reach if they allowed all buffs to be applied on pets.

Which content does this happen in? The biggest advantage that pet jobs get in this regard is the lack of weakness when their pet gets killed. It still doesn't change the fact that everytime your pet would be killed, it needs to be resummoned, rebuffed, and sent back out. Where do you see this becoming a problem?