It looks like about two thirds of the beach is owned by a charitable organization and actually leased back to the Town of Duxbury for use by the public.
Considering this, one would assume the town has a business interest in generating beach traffic that will benefit local business and help fund the lease. This interest would certainly be hampered if sunbathers and swimmers had to contend with people fishing.
So while it may kind of suck, it doesn't seem like this is a grand conspiracy against fishing.
Or, think of it this way...the taxpayers just funded you to fish on a mostly private beach until 8:30am
-spence