I tend to look at this on the other side. By the strict definition of national significance you used, the last weekend of the season will almost never have a nationally significant game, no matter whom we play, just from the sheer probability of elimination as a season progresses. Maybe now with a four team playoff there will be a few more chances, but still it will never be common to have two contenders playing. I think the fact that all of the recent IB have had at least one team in contention is astounding and great, and has given the game more national significance than any other end of season game we can compare it to. The fact that the game is also an in-state game, and an emotional rivalry with bragging right, makes it stupendously intense for both sides and not only for the contender.I think the days of the Iron Bowl being a big thing have regressed from what they were. How many times has the game carried any NATIONAL significance? 2013 obviously but what other times was this true? It did have some secondary significance (e.g. the unbeaten or one-loss team HAD to win but it didn't really mean much nationally otherwise). The only other time that comes immediately to mind is 1971, when both teams were undefeated, but I was two years old and have no recollection of this. OK, and maybe 1981 because of Coach Bryant's becoming the winningest coach (though this turned out to be a fraud when later research showed Pop Warner actually had won 319 games and so Bryant actually broke the record against Penn State in 1982).
The history of how it moved was interesting - and money-driven on both sides - but there's not much of interest now more than any other game save for rare years like 2013.
If we take just the last ten years and compare with other end of the season rivalry games, I think we have the most nationally significant rivalry by far. Of course, that is because we are the most significant team of the last decade. So I get it we can't give Auburn too much credit. But still I don't see how we can do better as far as a quality game goes. I sure don't want to play Vanderbilt the weekend after Thanksgiving. There are no teams in the west I'd prefer to play there than Auburn. I like LSU in November. And we can't schedule an east team for the last weekend, even if that is Auburn or UT, as any two teams who were really contenders would quite possibly play a rematch the very next week in Atlanta. That's a non-starter for scheduling. No non-conference team of any caliber is going to play us that weekend.
It seems to me it's either Auburn or we get a more meaningless and crappier game most years. I am not for that.