Your argument doesn't really make sense when applied holistically. If you wanted the government to only have easements for access to critical infrastructure (a telecom box in your other example), then you'd create a massive series of problems for right-of-way to public properties where access is cutoff from private properties.

Then the options become having the government take tons of small swaths of privately owned land by eminent domain to allow access to public spaces, or allow the landowners to cutoff access to public property for the sake of land ownership.

The existence of easements in part of common law to avoid those two extremes. It allows for the existence of a reasonable compromise without the need for excessive litigation.

The footpath is necessary because the public property (the coastal rocks) is cutoff from public access by the private property. It's no different than the many examples of public lakes being cutoff from access by private properties, and thus an easement is in place to allow the public to crossthrough private property to get to the lake.