Nah, natural beaches and navigable waterways should always be accessible to the public.
Then if your rich enough, you can always bribe the state official who determines if its a natural beach or navigable waterway.
Where I grew up, those who still held on to fragments of land grants passed down through the family still held riparian rights as well. The State of Maryland seized those in the 60s without compensation, even though those rights antedated the formation of ANY of the current governments or agencies exerting authority. Then it was ruled that the property owner (in a tidewater region) only owned down to the mean high water mark, and that anyone who wanted to could pull a boat up in front of your house, party and raise hell on the beach in front of your house, and when they left, they left everything from smoldering fire pits to broken bottles, condoms, etc. laying in what amounts to your front yard.
We have plenty of public land we all pay for. People who have waterfront property pay more for that in property taxes than those with frontage on paved roads, even though it didn't cost the government a dime to put the river in.
They also privately deal with the expenses of maintaining that property.
In this case I definitely side with the property owner.
If the public wants to have more public places, buy and develop those at public expense, rather than impose itself on private property.