I agree that destroying Vulcan is not that big of a deal if you take Star Trek as primarily a chronicle of the joint career of seven specific Starfleet officers. And I know that this is how a lot of Star Trek fans (and pretty much all of the, at best, casual Star Trek watchers) view it.
But for me, as someone who as always engaged with it at the much higher level of those seven people (then, with later series, different crews) simply being the lens through which a much larger universe is observed, destroying Vulcan is much more significant than killing any one of those seven people would be.
Plus, doing what I suggested so early in the movie would have hugely ramped up the suspense and feeling of real danger through the rest of the movie. Kind of like once they killed
you had an "oh ****, this could have real repercussions" feeling for the rest of the movie.