As someone with other fandoms that do involve alternate parallel realities/universes (Buffy/Angel, for example), this doesn't seem to be a problem to me.
In fact, I ADORE Buffy Wishverse fanfiction (you know, if everyone didn't die at the end). I am actually capable of caring about these alternate versions of the characters (as different as the characters become in episodes like The Wish/Doppelgangland, Birthday, Superstar, etc... just due to the tiniest of blips of alternate events in their timelines). The Jossverse is loaded with alternate realities almost identical to the Prime universe and a vast number of heavenly and hellish dimensions. Coming from this other fandom, Trek doing this didn't phase me at all.
Unfortunately, people thought this was time-travel rather than parallel-dimension hopping involving timelines which aren't concurrent with each other. Another concept familiar to those of us with a Jossverse background (16 years in Quar'toth = 3 weeks on Earth, 100 years in Acathla's Hell = 3 months on Earth, people growing to old age in the enslaved Anneverse within the span of 1 day, etc...)... And likewise, a few seconds in the Primeverse is 25 years in the Abramsverse.
One of the fun things about alternate realities is that they answer 'what if such and such happened a different way?' or 'what if a character whose life was altered met up with a different version of themselves?' This is just that. It doesn't make one a lesser character than the other.
Of course, Trekkies should be familiar with the concept of the "evil twin" doppelgänger which is essentially the '60s (and beyond) gimmick that the Mirrorverse was inspired by. Practically every sci-fi/supernatural/fantasy show PERIOD has had evil twins. It's as popular as trapping two characters together so they can work out their zany differences.
Trek has at least 3 alternate realities:
* the Primeverse
* the Mirrorverse
* the Abramsverse
Here's an explanation of alternate realities from another fandom (which is based upon the Many-Worlds Interpretation of String/Quantum Theory):
Anya: Sure, alternate realities. You could uh, could have like a world without shrimp. Or with, you know, nothing but shrimp. You could even make like a freaky world where Jonathan's some kind of not-perfect mouth-breather if that's what's blowing up your skirt these days.
The concept of a world with nothing but shrimp or the one just like ours but without shrimp is an idea of just how many alternate realities could be out there in a fandom that has already canonized the Many-Worlds Interpretation.
I think the root of the problem here is that people don't feel like another universe is equal to that of the Primeverse. In the new world, their world is as equal and real to them as the Primeverse is to the Prime characters. The characters are still the same people, but are living in changed circumstances. And these people might meet alternate versions of themselves who have been affected by different variables.
The fact that AU or "Wishverse"-type fanfiction exists at all shows that people can care about alternate reality versions of characters. Sometimes it's even more interesting than the well-traversed paths shown in the main reality.
What the deaths of George and Amanda and the destruction of Vulcan did was establish the new variables. It also showed that Abrams was willing to rip away the baby blanket/comfort zone of the complacent established universe. Things can happen very differently, new stories can be told and nothing is safe. It also gives a place for the characters to grow in different directions from their predecessors. Here we have an old Spock who, while he has lived with his planet and family intact, always remained more with his Vulcan side. This new Spock has the variables changed so that he is on his path to embracing his human side instead. It's an exploration of the character and where different choices would lead.
Even though the Prime Vulcan is intact, Prime Spock is still emotional over the loss of an alternate Vulcan regardless. That is the human response to seeing something like that, even if it is not logical.