While Loomis has his faults, I think he works well with his HC's. Loomis and Payton had a great relationship and Loomis was able to make money moves to get key FA's here if Payton wanted them. Loomis even worked well with Allen.
Yes we are strapped for money on the cap, but if a new HC comes in and really needs/wants a few players, I don't think Loomis would just say no unless there was no way to manipulate the salary cap to get said player or the player was just demanding too much money.
The Saints ownership under the Benson's have been pro-coach and player. There are plenty of teams like Dallas and Carolina where the Owner or GM run the team how they want and the HC has to play along. The Saints are not that way and any HC they hire will have his say on how to run the team and which players to keep, sign, or let go (again salary cap dependant).
Our main deterrents for an HC are obviously our salary cap issues, aging veterans we can't cut, and a small market.