Yep. NTCs and NMCs should be used on what GMs believe to be core players. A big reason why we're where we are is because at one point our core was 8-9 players (Sedins, Burrows, Higgins, Hansen, Garrison, Edler, Hamhuis, Bieksa, Luongo, Kesler) which is too many. I can't remember if we decided to honour Ballard and Booth's NTCs after trade right now either but I'll go with no just for arguments sake.
If you lose Higgins because he wants 4M then fine, you replace him through free agency or a trade. The answer isn't to give 2nd/3rd line tweeners NTCs to keep their salaries down.
You identify 4-5 players you want to build around and lock them up with NTCs/NMCs. The supporting cast, even if overpaid shouldn't be unless it's short term high performing players (Vrbata would be that).