I am going to look at this from a couple of different point of views.
The States point of view: The reason the hatcheries stock thousands and thousands of fish into the Salmon River is to attract anglers of all kinds. Trophy fisherman, Catch and Release and fisherman that eat fish. The fall brings the most amount of people over to Pulaski area. Not only does the DEC take in a lot of money from license sales but the small businesses depend on the fisherman. So if they close the spawning areas to fishing this may discourage people from going to these small towns and spending money.
Low income/lost of job: As we all know things are tight right now in our economy. Some people buy a fishing license so they can eat/feed there family. Some people do depend on filling there freezer to have food for the winter. When it breaks down to survival is it really that bad to take fish off there redds. Yes you can argue there is state funding for people out of the job but some people are to proud to ask for help.
The person who gets to fish a few times a year: Some people only get to fish a few times a year. They see fish and the try to fish for them they may not know they are fishing for spawning fish.
Old habits die hard: As Torrey said the great lakes fisheries has traditionally been a spawn run fishery. It was not that long ago snagging was aloud. Some people have the mind set that you can only catch fish that are on the redds. They think that spawning fish do not bite. That might be the case for salmon after they have spawned but not the case for trout.
My Opinion: I honestly do NOT care if people fish the redds. I think they should be practicing catch and release. But if they don't that is there right to keep any fish within the laws. I do not think it hurts fish to be caught of a redd and released back to it. I do agree with walking all over the redds is very bad, If the concern is so much about wild fish why don't we group together and take down dams and restore habitats. Its easy to give these people a hard time about there fishing ethics but not so easy to change the past.