Here's the thing.
Just because there are teams out there dumb enough to be in "cap hell", doesn't mean that with decent management it should ever happen.
The Saints, I mean, you've got
Drew Brees at 36 years old with a $26 million cap hit this year, they had to trade fragile
Jimmy Graham, whom they overpaid at 4/40 with 20m guaranteed, the corpse of
Marques Colston was due to make $6m before they restructured (to $3.8m is all they got him down to). For some reason they paid
Jarius Byrd 6/54 with 26 million guaranteed,
Junior Gallette is making more than $1m/sack.
Their punter...IN A DOME STADIUM...is making $4m/yr
Broderick Bunkley - $3.2 million for a 32-year-old JAG at best who can't stay healthy.
Jahari Evans - is a really good player, but $11 million cap hit for a guard?
Dannell Ellerbe is making $8.4 million this year. I think that's more than the base salaries for all the LBs on the Patriots roster combined. He'll be 30 this year.
Cameron Jordan- $7.0 million this year, 7.5 sacks last year.
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(Comparison career: Jordan - 64 GP 29.5 sacks, 5 FF, Chandler Jones - 40 GP, 23.5 Sacks, 6 FF. Jones went #21 in 2012, Jordan went #24 in 2011)
In other words, the Saints had no ****ing clue how to manage the cap, signed horrible contracts for (mostly) marginal players, and it bit them in the ass.
You have to be completely incompetent for an NFL team to get into anything resembling "cap hell". There are, sadly, many teams that can't math very well in their front office (Miami, for example). The Patriots certainly could never be confused for incompetent.