All Canadian teams show up disproportionately on these NTC/NMCs so to start off with all the Canadian teams should make a stink about it. Canadian teams have leverage as a good amount of the HRR comes from them (either via gate sales or via tv deals such as this). Bigger markets might also like the idea of turfing NTC/NMCs as GMs giving them out have hurt them (eg Rangers, Philly, San Jose) due to not being able to move said players and thus not maximizing the impact of their cap $.
Bigger markets should also want flexibility, NTC/NMCs don't really help them, it doesn't make it that much easier for them to acquire players and instead it compromises their flexibility as FAs that sign with them expect NTC/NMCs and they have no choice but to give it to them but in the process compromising their org's flexibility.
Everyone loses with NTC/NMCs... the smaller/rebuilding markets lose due to not being able to trade for impact players, the bigger markets lose being almost forced to give them out to remain competitive in the signing market and skewering their flexibility and future options, the NHL loses as trade activity is lower and thus fewer eyeball poppint trades, the fans lose with either not being able to get the best trade value for their trade protected players, or worse being stuck with them, or being unable to get a player that has that protection. The only group that benefits is the players.