The beach may be "public" but that doesn't give anyone the right to be a "vendor" there without the proper documentation and licensing. No one is questioning the Jamaican people's right to be there and enjoy the beach just like our right to do so.
If you go to a city like Kingston and see vendors setting up the entire width of the sidewalk and blocking rent paying, licensed to sell store owner's doorways and harassing patrons, you get a sense of what it is like when you don't enforce laws against illegal vending.
I like to buy pan chicken as much as the next person but there are health and safety concerns as well to consider. It is also true that most take safety and sanitary concerns seriously but when you open it up to any and all who want to cut an oil barrel in half to make a living then you also increase the risk.
Much of the reason that the beach has a vast majority of good "beautiful" people and not a majority of the ones that can occasionally be an issue is that there are laws that are enforced. Stop enforcing the laws then you will see a public beach become a free-for-all.
Just my opinion.