NFL doesn't circumvent the cap so much as they are permitted to use the old phrase of "Borrow from Peter to pay Paul", in that they utilize cap space in future years to pay for the player for the current year. The NFL allows teams to re-classify a payment to a player as a "Bonus" which can be allocated against the cap over multiple years to lower the cap charge for the current year, but adds future cap charges for the team to absorb later. Because their salary cap always (outside of the Covid year) goes up by a good amount. When the better players leave a team, they will have a lot of Dead Cap remaining. Brady was over $30 mill for TB to absorb when he was done, Cousins was $28 mill for Minny, Kelce/Cox for Phil was like $50 mill combined, etc. NHL fans are not accustomed to dead cap. They freak out about buying out a player or retaining on a contract for multiple seasons. NFL, there are more than a few teams with $50 mill plus of dead cap heading into 2025 season. SF/PHI for example.
NFL offers teams flexibility in adjusting the cap charges, but at the end of the day, each dollar they pay to the player has to hit their salary cap. NHL operates on the money that a player gets paid, has to hit the salary cap of a NHL team over the life of the contract. It's not based on who pays the player, thus rich teams can front load a contract and dump that higher cap charge onto a smaller market team later and actually end up having taken lower cap charges than the money they paid to the player. In the NFL, trading a player, like Seattle just did with Metcalf/Geno Smith, triggered Dead Cap for what remained unallocated for them for 2025.
I don't foresee the NHL adjusting how they do cap charges on the next CBA. Seems like they are not going to rock the boat in terms of most of the current CBA details. Will be some changes, but how they account for salary cap charges doesn't appear to be one of their main issues in negotiations.