While I was not alive at the time, I can answer that one to some degree.
1) Barnett never said anything as memorably quotable as Wallace's line about "segregation."
2) MLK didn't write a letter from the Jackson jail, he wrote one from the Birmingham jail.
3) Barnett disappeared while Wallace competed (okay, not the best word in 64) in the 1964/68/72/76 Democratic presidential primaries.
In 1968, in fact, Wallace was the biggest beneficiary of the assassination of Robert Kennedy. Wallace's poll numbers skyrocketed from what they were before that killing. According to the late political writer Teddy White in his book about the 1968 election, Wallace went from 9% of the vote in May to 21% in the September Lou Harris poll. To give you some idea about how hopeless Humphrey's campaign was......he did not run a single advertising spot on national radio or TV until October 24th (the election that year was November 5th). Incidentally, the Wallace vote of September went to Humphrey NOT Nixon, which should put to rest that nonsense about "the racist Southern strategy" of Nixon that never existed and has become ensconced as myth.
4) Wallace later got shot, making him more memorable publicly and his survival actually probably leads more folks nationally to recall his comments and associate two disconnected episodes with him as if they're one.
Plus - for better or worse - off the top of your head, how many OTHER civil rights wrongs besides the Mississippi Burning murders can you associate with Mississippi other than Ole Miss/Jackson State? And Barnett wasn't even governor when the MiBurn murders happened, Paul Johnson was.
Then look at this list:
segregation forever
schoolhouse door posturing
girls killed in the church bombing
Rosa Parks (Montgomery)
March to Selma
Bull Connor and the fire hoses
It doesn't take a genius to see why Alabama is more associated with it - and I'm guessing the fact we had a pretty damned good football team 1961-66 probably gave us a bigger name as well. (Btw - I wasn't meaning to insult you by the genius comment 81).
I find Wallace a fascinating guy just like I do Eugene McCarthy. They were mavericks in a different sense. Wallace was a politician through and through. A lot of folks don't realize that Wallace was
endorsed for Governor by the NAACP in 1958. He lost to John Patterson, who ran a segregationist campaign - and
Wallace vowed he would never be "out-segregationed" again (that's not the word he used obviously).
My favorite Wallace story happened in the 1976 election when he ran in a wheelchair for the Democratic nomination. (For the record, he actually carried the liberal city of BOSTON in that primary although he finished third statewide in Mass). Wendell Anderson of Minnesota shot his mouth off in a way you'll often see northerners view Southerners as "simpletons." Aiming his fire at Wallace, Anderson snarled that he would NOT support any nominee who would not promise in advance to support the eventual nominee and then worked in a reference to say that Wallace's "record on party loyalty is zero." Asked his reaction, Wallace turned it back on him by saying, "Well, is he gonna pledge up front right now to support me if I'm the nominee? I don't think I ought to be taking loyalty oath going one way."
And nobody tried that argument with Wallace again. But he had made his point.
In point of fact, I think the long-term overview of Wallace's impact on Alabama's politics and trying to advance them in the New South is mixed but positive. It is unfortunate that he has so quotable a phrase hung on him and that his entire life was reduced to a couple of anecdotes. It sickens me that too many non-Southerners don't know the FULL Wallace and hold him up in caricature. Make no mistake - Wallace was an avowed racist and playing a political game. He also softened later on and did a lot of good things. But maybe it's like Shakespeare said about the evil that men do living on after them and the good being buried with their bones.
And no, this doesn't make me any sort of Wallace apologist - I'm a historian of the scene, not an apologist, and I find the discussions here almost always fascinating, esp from those (Earle, Gray) who were around when this was going on. My mother despises Wallace for not sticking up for what he said were his convictions (and for his shameless trick of getting his wife elected governor in order to hold onto office). She was an Alabama native for her first 25 years and never got over his showboating in 1963 when she was a sophomore.