The NBA doesn't have a hard cap, their cap has exception rules is and is officially listed as a soft cap. Now one thing I do like about the NBA cap is they also have a minimum team salary and I think the NFL would benefit from that, most of the habitually bad teams in the NFL are also the cheap teams that don't spend up anywhere near the cap.
It took years for the Rozelle rule's abolishment to seriously effect the league, teams had key players tied up to long term contracts which delayed their entry into the new real free agency. By 84 free agency was in full effect and the predictions were by and large correct, the big market teams began to rule the roost. Not coincidentally that ushered in the time when the NFC, which mostly plays in larger media areas than the AFC and has higher team revenues, began their 13 year monopoly on the Superbowl with only 5 different teams hoisting the trophy, finally brought to an end by salary cap parity. Not only did these same 5 teams win over and over the tended to win in blow outs because they were the only teams that could afford to be that good. The NHL right now is in a period analogous to that 84-95 period in the NFL, the big market teams that can afford the most good players (with the exception of the Rangers who are just poorly run) have ruled the Cup and will continue to rule the Cup until some sort of competitive balance can be restored.
The facts are there and obvious to be seen by all, the era of the NFL when they had true free agency and no cap is the era of dynasties with a whopping 38% variation. So the cap has nearly doubled the level of variation and restored things to the same ball park things were in before the era of true free agency.
I appreciate your belated legwork on your rather shaky premise.
Your belief in the beneficence of a hard salary cap boils down to a ten year period in the NFL that provides little hard evidence of such a preposterous claim.
You salt your hypotheses with words like "...were by and large correct...", "...over and over the(y) tended to win..." and other such fuzzy foundational statements, followed by absolute concluding statements like "...the only teams that could afford ...", and "...true free agency and no cap is the era of dynasties...".
Now, I don't mind someone searching out facts to back up their preconceived ideas, but the facts should be sturdier than this if you're going to make baldly absolute statements about cause and effect.
In the miniscule slice of NFL time upon which you've hung your 'theory', 1984 to 1995, you had SIX different teams (Los Angeles Raiders (unless you're discounting the 1984 Superbowl), Wash., NY Giants, Chicago Bears, San Fran, and Dallas). Of those, San Fran and Dallas are hardly the population meccas of NY, LA and Chicago fame. If size of market were the critical dimension of success, where were the NY Jets and the LA Rams? Certainly no lack of money in those cities, was there?
So it boils down to a perception that you have that free agency was a demon to be exorcised based on the extremely tenuous proposition that because the Giants won 2 in 5 years, the Redskins won 2 in 5 years, the Bears won 1, and two smaller market teams (SF and Dallas) won 3 in 6 and 2 in a row, respectively.
Based on this flimsy logic, a great case can be made that the NE Patriots are proof that the current hard salary cap promotes the status quo. They have, after all won more Superbowls in 4 years than any team other than Dallas (3 wins in 4 years, too).
Face it. You're unable to support this hard cap lunacy with anything even remotely looking like hard data.
Just because you believe it, doesn't make it so.
BTW, the reason that the NBA is now not "officially" a hard cap (I wonder who made that "official" decision anyhow) is because it was so problematic that the league started creating exceptions to make it workable.
If it didn't work in the NBA, why impose it on the NHL? The problem in the NHL is that the owners are completely incapable of controlling their checkbooks. "Please, stop us from writing more checks. Please!"
They get no sympathy from me, especially when Tampa and Calgary show up in the Finals last year (with marginal salaries paid to their Cup-hungry players).