Actually there seems to have been a lot of hints now that most of what helped Tevinter rise to power came from the elves. Either stuff they found in ruins or from elven captives. So without the elves it is unlikely the human nations would have advanced as quickly as they did. The Core Rule Books suggests that it was elves who taught the Neromenians how to use lyrium and it was this that gave them a head start over their neighbours. The lore of the Fog Warriors on Seheron suggests that their ancestors "learned at the feet of the elves". Felassan says that the column glowed with runes "that the fools in Tevinter copied by rote like children tracing letters". This latter column would seem to suggest that in a lot of cases the human mages simply came by their knowledge by trial and error and probably never fully understood it. Had Solas not intervened, it is unlikely the humans would ever have been in a position to challenge the Evanuris. As Imshael said, you "Always have to respect old elven magic."
It wasn't just that the humans had a head start, raising the Veil did something profound to the elves, even the ones born pre-Veil. Those born post Veil were handicapped by their isolation from the outside world, which I think was largely due to those born pre-Veil still controlling them. We still don't know precisely what happened in the confrontation in Arlathan Forest but I doubt there were any pre-Veil elves among those captured by Tevinter. Then the post-Veil elves became slaves to Tevinter who deliberately tried to eradicate all knowledge of their earlier culture. Could this be because they feared what the elves might be capable of if they recovered it? Considering that the majority of modern elves have only been free for a short time and even the Dalish have been living on the fringes of society, trying to piece together magical lore, they haven't done that badly. They are certainly no further behind, say, the Avaar in what they can do with their magic.
I find it interesting to see how magic developed among human communities like the Avaar and the Rivani, compared with the Neromenians. The Avaar (who are descended from the original tribes in the south) have been around just as long as the Neromenians and yet their magic is far more limited and doesn't seem to have changed much in the succeeding few thousand years. The Neromenian belief that their heroes were reborn as dragons seems very similar to the Avaar belief concerning Hakkon. Both Avaar and Rivani have a different relationship with spirits that is in fact much closer to what the ancient elves seemed to have. The only thing that seems to have made the difference between the humans in terms of magic is that the Neromenians had greater access to elven artefacts and actual elven teachers. I do wonder if originally the elves that helped their rise to power did so willingly because they saw them as a way of challenging the remnant followers of the Evanuris. Still, what gave the Neromenians their head start definitely came from the elves and that is what gave them their superiority in magic over their neighbours, that the descendants still benefit from today.