re: Realistically, how often should a Football Program like LSU win a Championship?

Contending every few year and reaching the playoff multiple times a decade is clearly doable here, so anything less shouldn't be accepted.

We will inevitably go through stretches where we don't as every top program does, but that should balance out with decades where we do better than what you mentioned

List of all final AP polls so you can get a reference historically of how often we have been playoff caliber

Would've been in "playoff discussion" (top 10):
34: #8
37: #2
38: #8
46: #8
49: #9
58: #1
59: #3
61: #4
62: #7
64: #7
65:#8
69: #10
70: #7
71: #11
72: #11
82: #11
86: #10
87: #5
01: #7
03: #2
05: #6
06: #3
07: #1
10: #8
11: #2

-had to include years #11(3), one away bugged me.
-this is post bowl season so bowl losses could have dropped us out when we would have been in hypothetical playoff
-90s would have been only decade we never contended, highest finishes 96: #12, 97: #13

This is by no means perfect, but a decent way to gauge our program historically

We've finished in the top 10 roughly 30% of the 82 AP polls even with the 90s slump. With our current brand being among the blue bloods I think we should definitely not settle for 4+ year stretches without a serious run at the playoff if not an actual appearance.