I'm biased I will admit but I was thinking more 80's Mid South meets early 90's WCW than Thesz or UWF International. Not after watching Brock vs Cain. Just minor details like cutting out spinning DDT's, more emphasis on psychology and outlawing closed fists. Dynamite Kid and Bret Hart were the masters of the 'liitle details' approach that I feel would have benefitted them in the long term. As you describe, WWE has the monopoly on semi replaced cartoon larger than life characters with cartoony indie style athleticism.But no us televised promotion have ran a serious in-ring approach since 1984.
There is a universe sized gulf between the in-ring style of the 1950s guys like Thesz and Buddy Rodgers and say Hulk Hogan vs Ultimate Warrior or Undertaker. They couldn't be considered same form of entertainment even, Thesz and Rodgers is closer to modern mma.
I know some hardcore fans hate Indy style but that's far far closer to Hogan/Warrior/Sting/Undertaker/Flair cartoon stuff than it is to the Thesz/Lewis/Rodgers shoot style.
AEW has been very inconsistent in some ways. They have Cody, Arn, a ranking system, time limits, statistics etc. Yet Nick Jackson takes a beating from 4 men and sells it for a 30 seconds.