Couple of things here:
1) The NFL model will never be like the MLB model because the NFL broadcast pool is a) HUGE and b) almost entirely centralized since 100% of football games are broadcast by one of the participating networks. iow, aside from local radio rights (a teensy weensy portion of the whole) there's not a lot of difference in the broadcast incomes of teams. By contrast, baseball's central broadcast money is evenly distributed just like the NFL's. But then each team also has its own local TV/radio deals which can vary widely and represent a much larger portion of the whole. So unless you're going to pool all that local money and then split it up evenly there's always going to be disparities. Now pooling all that local money is never going to fly with the larger market teams. Plus, if teams were only going to hang onto 1/30th of any new monies they earn via local media, it would remove all the incentive for clubs to strike better deals for themselves or to do things like start their own networks (YES, SNY) or streaming services. It would be a big dampener on both incentive and investment.
2) Of course the ultimate goal is salary suppression. They'll call it 'cost predictability/stability' or some such pseudonym but, yeah, the idea is to limit the cost of labor overall and set it on a predictable path from year to year. And I've harped on this for years now: there's no correlation between a cap and so-called parity/competitive balance. The NFL, which not only has long had a hard cap (no exceptions for incumbent players like the NBA) and has consistently had more teams in their playoff tourney as compared to completely cap-less MLB, has had Fewer Super Bowl winners, Fewer Super Bowl participants, and More franchises on the outside looking in (defined as those who have failed to reach a conference/league final ... iow, be a Final Four team) than MLB has had WS winners / participants / and non-final-four teams. You'll hear it said often that it's the complete opposite by those who simply assume that of course a cap increases parity (or by those who think part of their job description is to parrot whatever the NFL tells them) it just doesn't happen to be accurate.
In this century, the NFL has seen 13 different teams win a SB (43% of teams), 20 different teams play in a SB (62.5%), and has five franchises which have not played in an NFC or AFC championship game (15.6%). In MLB those numbers for the same time frame are 16 (53.3%), 22 (7.3%), and 2 (6.7%)
* SB winners: Seahawks (2), Eagles (2), Chiefs (3), Rams (1), Buccaneers (2), Patriots (5), Broncos (1), Ravens (1), Giants (2), Packers (1), Saints (1), Steelers (2), Colts (1).
SB participants: All except Redskins/Commanders, Cowboys, Lions, Vikings, Bills, Dolphins, Jets, Browns, Jaguars, Texans, Chargers. Raiders
No conference championship games: Texans, Cowboys, Raiders, Dolphins, Browns
World Series winners: Dodgers (3), Rangers (1), Astros (2), Braves (1), Nationals (1), Red Sox (4), Cubs (1), Royals (1), Giants (3), Cardinals (2), Yankees (1), Phillies (1), White Sox (1), Marlins (1 ), Angels (1), Diamondbacks (1)
WS participants: all but Brewers, Reds, Pirates, Padres, Orioles, Twins, Angels, Mariners
No NLCS/ALCS: Reds, Pirates