I may be missing something or misremembering something but my understanding was that that alternate future was doomed anyway - all of those people were going to die no matter what G'raha did or didn't do.
And in the long run, that alternate future's existence meant the Ascians won - the first was destroyed, the calamity wiped out the WoL and company, which leaves very few people that I can think of who'd be remotely powerful enough to stop the Ascians from doing the same thing again and again until their final plan succeeded, and the final rejoining occurred. As far as I can tell, their options were to change the past or live out a doomed future.
What I like about this is that this isn't a black and white good vs evil situation - the difference is subtle, and lies in intent. G'raha didn't know if his actions would delete or branch off from that bleak future, but he had a chance to stop things from even getting that bad in the first place and he took it. Heck, I'm sure if the Convocation had known how, they may well have done the same thing instead of summoning Zodiark and rewriting reality. Both extreme solutions to catastrophic, world ending events. Both carried out with good intentions.
The Ascians don't know or care what the new world, our world, could be like if left alone. They've been set on deliberately destroying everything that's been built to bring back the past - they know for a fact their success means the death of every single living creature in all of the shards, and their motive is to save the lives they deem as worthy enough to exist. Whereas G'raha and co. want to save the worlds they saw spiraling directly to a grim and grisly end. I'd compare his actions more to the Convocation's when their world was ending than to the Ascians/Emet today really, and whether it was the right choice or not at least partly comes down to perspective - and may be impossible to know for sure.