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I could be wrong about this but I don't think Bama or its fans consider LSU a big important rival.  Not in the sense of AU or UT.  LSU (and fans) almost certainly care more about playing Bama than the other way around, although for any sort of traditionalist they're still not in the same realm as Ole Miss.  I suspect Alabama could take or leave LSU and wouldn't care much. 

The perma-rival schedule I saw that had us with Ole Miss, A&M, and Alabama is about as good as we could ask for.  I'll never enjoy losing AU as an annual game (the most objectively crazy series in the country this century, by far), but I wouldn't exactly want to trade Bama for them.  Same for Clanga, there's a ton of history there but I wouldn't swap Ole Miss for them.  So we get what we get, and if that's what we get I'd say that's as good as we could hope for.

Which is what makes me think it's almost certainly going to be one of the dumber models such as one that had LSU with OU.  The conference has a habit of making Baton Rouge feel like it got the middle finger.

You're probably right. I didn't think that LSU ranked up there with Auburn and Tennessee, but, perhaps afflicted with recency-bias, I thought LSU was probably #3.

You know who doesn't have two? OU.

Missouri probably doesn't have two genuine rivalries either, which is probably why many of these prognostications show OU-Mizzou as one of the "permanents."

OU of course played Missouri for a long time--96 games (67-24-5), starting in 1902. But Missouri's biggest rivals were (1) Kansas and (2) Kansas State. And OU's biggest rivals were (1) Texas and (1a) Nebraska. OU fans didn't like going to games in Columbia, because they thought that Missouri fans were jackasses. But that didn't make the "rivalry" anything special.

OU and Arkansas have played 15 games (10-4-1), but only 3 times since 1926. And Arkansas has a longstanding rivalry with/hatred of Texas. I think Arkansas will be one of Texas' permanent rivals, but not one of OU's.

OU and Texas A&M have played 31 times (19-12), and I think that a lot of OU fans would like to see the Aggies on the schedule. But I don't think that OU would be A&M's preference and I doubt that the SEC will make OU-ATM a permanent.

Other OU vs. SEC series:
Alabama 6
Auburn 2
Florida 2
Georgia 1
Kentucky 3
LSU 3
Ole Miss 1
Mississippi State 0
South Carolina 0
Tennessee 4
Vanderbilt 3

So, obviously, OU-Bama should be a permanent.

There's probably a generational divide re: AU/aTm amongst LSU fans. 

All ages probably want to see Alabama kept on the schedule.  For older fans, Bama is the decades-old measuring stick and the big name that demands outside attention when they play.  For younger fans, Bama is the roadblock to goals, the video game boss at the end of a level you can't advance past without beating.  Worth noting that these younger fans didn't care much about Bama before Saban got there and they languished for a while.  That bears thinking about because Bama won't always be BAMA. 

The older folks will want to keep aTm to resume such a long-standing ooc rivalry--A&M has played LSU more times than about half of the SEC teams, or something like that.  The Youngers didn't pay much attention until after that game had gone away and still feel weird about ending every year with the Aggies.  They grew up on Barn-fires, band-fights, stomp-gate, etc. and will want Auburn's sorry carcass trotted out every year to focus their rage on.  The Olders likely think of AU as an interesting game, but if it gets dropped to only half the time, no biggie. 

If the goal were to satisfy myself only, I'd probably keep both AU (for the hates) and A&M (for the historyz) and boot Bama to 2-of-4, not because I don't like the game but because it's just lower down the list.  From what I can tell I'm in the minority.  Most LSU fans would spaz if an annual Bama tilt were taken from them.  
One thing we can all agree on is that Ole Miss can geaux to hell

Ranking the most iconic SEC football stadiums from worst to first (usatoday.com)

Heh, for you SEC newcomers, a brief synopsis of the various stadia, mostly ranked here by capacity (I love rankings).

I've been to four of these in person, Kroger Field at UK is fine IMHO.  Maybe it is next to last, dunno, whatever, but it's fine.  Ole Miss is fine also, overshadowed by the TGing though.  I thought Neyland needed some updating which is happening, and Sanford needs some as well (which also is afoot).  Older stadia often lack simple things like enough bathrooms for ladies etc.

Ranking the most iconic SEC football stadiums from worst to first (usatoday.com)

Heh, for you SEC newcomers, a brief synopsis of the various stadia, mostly ranked here by capacity (I love rankings).

The descriptions were more about game-day atmosphere than about the stadiums themselves.

Speaking of "lists" I disdain, 

College footballs top 35 coaches ahead of 2023 season, ranked: Kirby Smart grabs top billing (247sports.com)

I know this is click bait, but some coaches simply have a lot more to work with than others.