First off, I'll refer to snagging as the intentional foul hooking of fish which is illegal under the regs, and not the legal technique of flossing.
However, the result of this is that there are plenty of fish that are intentionally foul hooked in the caudal fin, pectoral fin, dorsal fin, gill plate, anal fin, and eye socket that are released back into the wild. The "angler" would then release said fish because it is not a "head shot". The consequence is that several fish are depleted of their energy reserves, mishandled, dragged onto the rocks, and then kicked back into the water. Ultimately the "angler" would remain at their post, snagging away until their limit was reached. This may result in many more than their limit of fish dying or being so depleted and abused that they would be unable to spawn or compete for access to spawning grounds. The ultimate end result is an effective withdraw of perhaps many more than 2-4 salmon out of the system, but could be much, much higher. In the broad strokes, if all "anglers" who practice snagging are releasing non "head shot" fish, the implications for a fishery may be much larger than if we simply allowed them to keep fish hooked from any location.
I think your intentions are good and your proposal would probably have the desired effect on a some small percentage of anglers but overall I think it would not have the overall end result you envision.
We should not reward unrespectable behavior by allowing people to benefit from those actions. I feel that would open the floodgates to blatant snagging on all systems all the time if it were legalized and would spread like wildfire if legitimized in any way shape or form.
IMHO most people are ethical and try to learn to do things the right way but there is a portion of the fishing community (possibly larger than we realize) that would absolutely explode if keeping snagged fish were allowed. Believe you me, that sub-segment of the community are not too concerned about resource management, conservation, and respect for fish. Allow the retention of foul-hooked fish and we'll have lost any leverage to convert the receptive ones about selective techniques and appropriate methods.
Current snaggers will then go off and teach their friends, families, kids the only 'proper' way of fishing they will probably ever know. Would they ever bother learning any other technique if snagging is suddenly legal?
I agree current enforcement currently leaves much to be desired, but at least the current regs gives us regular people some ammunition and basis with which to educate whenever possible, and call out/report violators.
It's no secret that these "anglers" are intentionally, willyfully, and very purposely foul hooking fish - many times they don't even have a presentation on their hook. Yet they do so with impunity, and still retain only those fish hooked in the mouth. My suggestion is that if we are going to let them exercise this type of behavior as we currently do - we should allow them to retain fish hooked anywhere on their body so as to satisfy their daily quotas, prevent the foul hooking and subsequent release of other fish, and get them off the resource.
If we want them off the resource, I firmly don't believe that the answer is to reward such behavior and hope they go home early. They'll just be back the next day and in greater numbers because it's so darn easy.
From a human psychology perspective, people respond to incentives. If you want to reduce a behaviour, you have to reduce the incentive in doing it or make the alternatives more desirable; not make it even easier to do and rewarding.