Bobbi was maybe the most loyal SHIELD agent of all

* I don't know where the hell you got that idea.  I've never proclaimed any sort of loyalty to Fury.
** That's not what I said.  I said she was loyal to her idea of what she thought SHIELD should be.  And then helped lead an effort to conduct a coup d' etat.

I never disputed they defended their ship. Actually my point was that the defense of their ship (and Calderon helping at the Academy) was the only Hydra fighting we saw them do. Meanwhile SHIELD was trying to protect/save the world. You're drinking Gonzales Gang Kool-Aide.

And now, lets take a moment and analyze Coulson's SHIELD, from the time Hydra came out of the shadows, until the two SHIIELDs re-united. I don't see much real action against Hydra that was not based upon revenge against Ward/Garret, and other than that nearly everything they did was related to the obelisk and the alien city.
Revenge on Ward and Garrett?  Garrett was dead and Ward, who was in their custody, had escaped thanks to his stupid brother.  Why wouldn't the Good Guys want to apprehend the country's "most wanted"? Who, by the way, had rejoined Hydra.  Are you starting to see a pattern, here?  Here's a hint:  HYDRA (not alien obsession).

So... NOW... let's take a moment to analyze what actually did happen in S2:
We saw SHIELD on a mission to acquire intel on an item that was stored in The Fridge. On that mission was a Gonzales Gang spy (Hartley). Were they on a mission to get the intel because it satisfied Coulson's supposed alien obsession? No they were getting the stuff that was liberated from The Fridge to get it off the streets and keep it away from Hydra. Come to find out the intel was for an 084 (kind of important). Oh, wait...... not just an 084, but the first one ever. He didn't know about any alien connection all he knew from Fury's toolbox was it was the first one, it was extremely dangerous and he didn't want Hydra to have. So it wasn't about alien crap it was about keeping the world safe. He was also working against Hydra by having Simmons undercover to get intel (Aad don't even think about comparing Simmons undercover in Hydra to Hartley undercover in SHIELD as they are two different things. SHIELD working against a known enemy and the Gonzales Gang with the singular focus of taking down SHIELD).  They also protected a military General from being kidnapped by an enhanced Hydra operative, Carl Creel, whom they later turned over to said General.  So SHIELD had at least a bit of legitimacy by their relationship with Talbot while the Gonzales Gang had none.  They were operating in the shadows with the singular focus of taking down SHIELD.  You show me any other thing they did other than spy on and attack SHIELD. ANYTHING they did to fight the good fight. All we ever saw was them devoting all their resources to take down SHIELD. Sounds like a terrorist group to me. Sure they thought they were the good-guys, but Hitler thought he was the good-guy, too.

The difference between the Gonzales Gang attack on SHIELD and the Cybertech take-down are so blatantly obvious, I'm surprised you need clarification.
SHIELD took down Cybertech, Garrett's new HQ, because that's the place that actually developed the centipede serum, super soldiers and that Deathlock guy that they made punch off the head of a drug cartel leader in South America. Oh yeah, don't forget that rib-ectomy that happened either..........  In short - SHIELD, the good guys, did what SHIELD does - stopped evil.  The Gonzales Gang tried to take down the guys that protect the world from evil.

As for alien obsession - yeah he was carving but he wasn't obsessing over it.  He was trying to deal with it while SHIELD did what SHIELD does.  He didn't obsess until The Writing on the Wall, which was the episode in which he was cured.  The mission to Puerto Rico was to stop Hydra from taking the Obelisk to the alien city not to appease his supposed obsession.  Like I said, you're drinking the Gonzales Gang Kool-Aide.