However, the problem would be that the amount of teams every year would change, which I am not sure would work so well. I tend to be one of those people who likes nice round numbers. Another small problem I foresee with this is that it puts an immense amount of pressure on the top teams to do very well so their state can get the bonus spot.
The number of teams every year can change a little anyway, depending on the facilities, funding, etc. Some years it's actually less than 60 anyway.
As for the pressure bit, there's already a tremendous amount of pressure on the front-runners to place as high as possible at Nationals- it's always been a high-pressure competition for those who think they have a chance at medaling. I don't think this method would put any considerably greater amount of pressure on anyone.
Just an idea- this year, the 1st place team was way ahead, but 2-11 were very close, and then 12+ was all further behind. I haven't verified this with other years' score sheets, but I think it's not uncommon for it to be unevenly spread like that. I don't know if this would work, but it might make sense to choose how many teams get one added for the next year based on these point groupings... as in, if this were hypothetically implemented this coming year, the states of 1-11 would get another team, because they were clearly ahead of the next few teams based on overall scores. If one year, say, the top 9 were really close, and then there was a big gap before the 10th, then 1-9 would get an extra. If it was more than 12 before you saw a serious gap like that, then only the top 12 would get it, I guess. A "big gap" would have to be specifically defined... I don't know, more than 30 points? 40 points? Something like that, I'm not sure what would work the best.