A common criticism about ME2 is that it didn't advance the central story of the trilogy, the Reaper War. Isn't this hindsight?
No, because most of the criticisms were apparent even before ME3.
The implications for killing the companion cast (that they couldn't be very important going forward), destroying the Collector Base (it can't be that important if it'd screw over the larger half of the morality spectrum), and having no actual set-up for beating the Reapers were apparent well before. Even the question of why the Collectors were abducting people for the Human Reaper was a linger plot hole of ME2's own creation, given that the ending and Arrival showed that the Human Reaper wasn't some Sovereign 2.0 to retake the Citadel.
How can ME2 be blamed for not advancing the story if ME3 did not utilize the 2nd game's plot points AT ALL?
Because ME2 didn't have many plot points, it had vague techno-babble, and didn't have any idea of how it wanted them used going forward.
The writers were making it up as they went along- the point for planning doesn't begin after you've made your mid-trilogy work.
I know I'm personifying the two games but really they don't feel related. Is it the fault of the preceding game or the sequel?
Not feeling related is the problem, and why
A trilogy requires structural support throughout the entire effort, so that the ending doesn't get bogged down with the weaknesses of the early/midgame. ME2 didn't support it the end-game plan, because there was no plan- but that should have been established at the point of ME2, not ME3. ME2 is responsible for setting up ME3, not the other way around.
You don't blame the last man of a relay race for losing if he has to make up more than his fair share of time.
I am playing through the trilogy again and having started ME3, I see Cerberus being active in every frakking theater of war like they're some super convenient super organization that can do everything. Yes, there is the explanation at the end that TIM has been indoctrinated but I personally feel it was a cop out and very contrary to Cerberus' paranoia shown in ME2.
However good ME2 is, I now wish that the 'schism' with Cerberus was resolved in ME2 itself, with the 'save or destroy' Collector base in the middle of the game and an assault on TIM towards the end. Something like Witcher 2 with it's two branching storylines finally converging again at the end.
It was, and it was a weakness- that discongruity is reflective of a lack of the planning ME2 had, because ME2 didn't decide what it wanted Cerberus to actually be or where it intended the series to go. It threw up a lot of ideas to be picked up or dropped, rather than setting up a plan.
I play ME2 with all these great characters and marvel at the potential that was squandered going into ME3. IF Shepard can have plot armor, why not Miranda? Jack? Grunt? Garrus? Tali?
Because ME2 built itself around something called the Suicide Mission, with the sales pitch that anyone could die. Shepard's death was explicitly non-canon even before ME2's release, while squadmate deaths carrying forward into the future was a feature.
The thing about making a character even potentially killable is that all future plots have to be written with the condition that the character is, well, killed. You either duplicate resources for alternate paths- entirely new voice actor costs and writing for things like Mordin's replacement, Jack's mission, or the Quarian plotline- or you diminish the importance, or both. Note how Garrus is completely plot irrelevant if he's missing, and how Tali's seemingly vital role only shapes the end-Rannoch choice.
ME3 is a poorer game just by comparing its squad roster to that of its predecessor.
ME2 kneecapped ME3's squad roster by inflating the costs of using any of the old squadmates.
I'd also argue that ME3 does a far better handling of it's individual character arcs than ME2 did. The depth and polish on the squadmate conversations and characterizations is signficant: even without loyalty missions dedicated to the character (and rarely the trilogy plots), the companions we got talk more on the ship, talk more with eachother, and there's far more interaction amongst the cast in the course of missions themselves. ME2 had a particularly nasty habbit of only using interchangeable filler grunts or snark from its companions- ME3 has entire squadmate exchanges tailored to the plot missions and personalities.