Technically I don't understand what complaint small market or badly managed teams have. In addition, they apparently don't like that good teams are competing with them for LTIR contracts because thats how some of the badly managed/small market teams have met the cap floor.
The players are paid for their regular season service. The salary cap controls SALARIES DURING THE REGULAR SEASON ALREADY, and a team that temporarily benefits will have to be cap compliant by the first day of the next season. If a player (typically with term) is put on LTIR he doesn't play, and the team does not benefit from his skill. On the other hand, if a skilled player is traded at the deadline (typically on an expiring contract), he isn't paid during the playoffs by his new team either. Since players are literally not paid for their service during the playoffs, this could be solved by e.g., limiting teams with LTIR protection to only trade for players on expiring contracts. But that isn't the issue here obviously. The LTIR system is probably viewed by some as contributing to an increase in player compensation and must be fought because, e.g., guys like Seabrook won't retire.
In a sense, the current LTIR system works as a small residual bonus/protection to good teams and skilled players whose contracts are typically expiring. It allows a team to sell a bad contract to another team, and allows good players to go to another team and play for a championship. The owners should either leave the system as is and normalize it (by, e.g., not tying it to injuries and expanding it to underperforming veterans, or not allowing basement teams to meet the cap floor with LTIR contracts), or pay the players in some way for a benefit they would lose. I kinda like how the better teams have transacted in LTIR contracts because IT BENEFITS WELL MANAGED TEAMS AND GOOD PLAYERS WHO EITHER BECOME INJURED/OLD AND CAN'T PLAY OR ARE ON AN EXPIRING CONTRACT).