Although the idea may seem abhorrent to members of the public the state should not feel pressured to act in an ad hoc method to appease popular opinion. The United States has long been an advocate of capitalism and as such wealthy citizens have rights to enforce and benefit from their property ownership however they see fit.
If the property was legally purchased by this billionaire, then he should retain the rights to it. The state has no right to forcefully take that which belongs to an individual except in extreme circumstances. Unless there is no other reasonable alternative for accessing the beach, the government should be willing to meet the demand for fair compensation of the owner.
No state is justified in taking the right of way by eminent domain of this type of case. Eminent domain has traditionally been used as a mechanism to take private property for public use for projects that serve the public good, such as roads, bridges and so on. When used for private purposes, it amounts to nothing short of an illegal taking.
Private property is something that is sacred in the United States. Our land was built upon the right to own property. For the Government to take away any person's personal property without deserved payment is not acceptable. Eminent domain gives the government the right to recover property, but payment is required.