Why do the Patriots have so much financial flexibility this season - that they could sign a top-of-the-market free agent to a Super Bowl roster, bring in a bunch of young veterans in exchange for cheap draft picks, and still sit on plenty of available cap space?
They have essentially no players who are overpaid and no significant dead cap space.
You can point to most rosters and see outlying contracts consuming a lot of cap space, or the correlating dead cap money from releasing those players. In the past, you could argue that the Wilfork contract, the Mayo contract, or other (high-performing) veterans that signed market-based deals but restructured over the years had contracts that exceeded their current value.
Mayo was on the books for $4.4mm in 2016 in dead money.
Revis, Mankins, and Arrington consumed about $12.5mm in dead money in 2015.
And so forth.
It's hard to point to a contract currently that looks like an overpay. Solder or McCourty at $11mm each? Not bargains, but not really out of market for core players.
I think once you get to this point, you aren't juggling contracts, pushing money out from the current year to the future, and then facing the same problem again the next season.
Maybe it starts with Brady's willingness to play well below top of market, and the impact it has on some other core players. Maybe it's partly focusing on lots of B+ players - Cannon, Guy, McClellin, Harmon, Branch. Maybe it's a lot of veterans who want to play for a winner - Edelman, Ninkovich, Amendola, Chung - at deals below market.