I have seen the relegation and promotion system suggested by some (mostly European I presume) NHL fans. How does that work? If a team were relegated, does that mean they miss out on a team like Colorado or Tampa coming to town during the relegation period?
If so, I don't think American fans would buy in to that at all.
The best analogy would be using the AHL if it wasn't a developmental league affiliated with teams, but rather an independent professional league. So in this scenario the AHL could bid on the same free agents as the NHL, but they mostly would lack the financial firepower to compete with NHL teams due to smaller stadiums, lower prices, and so on. They could probably compete for bubble guys though, or maybe offer guys like Lewis or Clifford top dollar to lure them away. There is no cap in any of the leagues. Also, you can buy players from other teams, so in addition to paying their salary, you have to pay the other teams for the transfer. For example, Toronto could buy Doughty by paying the Kings $40M, which the Kings could reinvest in other players.
At the end of each season, the bottom 3 teams in the NHL would be relegated to the AHL, with the top 3 AHL teams promoted to the NHL. So regulated teams would no longer play NHL teams, but San Diego, Bakersfield, Ontario, etc. The top AHL teams would play an NHL schedule.
The money difference is huge because of TV revenues, so once you hit the NHL you would want to stay there. So basically you have of teams. Ones who would spend whatever they could to get top players and win the Cup (NYR, Toronto, MTL). Then a 2nd tier who would spend to try and be competitive, but more efficient and not just throw money around (LA, Chicago, Boston, Philly, Detroit, maybe Vancouver, Pittsburgh, Washington). Then a third tier of teams who might not never challenge for a cup, but is comfortably safe in the NHL. Your fourth tier teams would be those who don't want to spend (or don't have) the resources and are usually threatened with moving down (Florida, Islanders, Arizona, to a lesser extent Buffalo, Carolina, and Anaheim)
Parity takes a huge hit in a system like this, but at the same time there are big incentives to stay in the top league so your bottom teams are pressured to spend more. It would be a huge change of what people are used to.