I think you are ever simplifying the situation drastically. Every year, when you look at the 8 (now 10) teams that make the Playoffs in MLB, there are ALWAYS a mix of high and LOW payroll teams. And BTW, the Cardinals were ranked SEVENTH in the National League this year in payroll. This year you have Oakland, Tampa, Pittsburgh, Baltimore and Kansas City way down the list in payroll. You have teams such as the Astros, Rockies, Brewers, Rays who have all had their share of post season appearances. While high payroll teams such as the Red Sox, Dodgers, Cubs, and Angels have had more than their share of losing. You site the Yankees as the biggest culprit in "buying" championships, but how have they done in that 30 year period you reference? Other than the 5 year period in the 90's (they won 4 out of 5 years), they have won ONE other time.
That also has NOTHING to do with the NFL and the Rams being one of the annual bottom feeders. If anything , the salary cap, and the built in parity which is the very definition of what the NFL strives for, just exaggerates the point in the Rams case. They were one of many examples of "worst to first" that exists in the NFL, and yet, be it in the 90's or this latest decade of futility, they just can't seem to get out of their own way. But yet, teams like SF, New England, Pittsburgh, Green Bay can somehow figure out the formula to be contenders year in and year out. The same opportunity is there for the Rams. And to somehow insinuate the salary structure of the Cardinals coaching staff somehow tilts things in their favor, when ignoring the Rams coaching staff is among the highest in the NFL, to me is cherry picking and not even privy to this discussion.
The BIGGEST advantage if you ask me the Cardinals enjoy over most of the competitors is stability. They have had TWO Managers in the last 20 years. They have had TWO GM's in that same time period. They have an organizational philosophy that is clearly defined, and they stick to it. If and when the Rams get to the point where they aren't a revolving door of coaches, and constantly in a "rebuild" mode, then maybe they can enjoy some of the same success. So rather than detest the Cardinals for all of their success, and somehow try to imply they have advantages that ANY NFL TEAM doesn't have, I choose to applaud an organization who consistently manages to make wise business decisions, has a top notch scouting department, develops home grown talent and just plain WINS.