As luck would have it, the Economist has an article, "How the seaside emerged as the holiday destination of choice", by "Prospero".

It doesn't start with ancient beach visits, discussed in the thread Did ancient peoples "go to the beach" as we do today?.

It doesn't answer why sea-bathing wasn't popular, but just talks about the modern development, which they date to 18th C England. It starts with the bathing machine in Britain from the 1730s, "a small cabin on wheels" to allow sea-bathing in privacy. The bathing machine spread across Europe, as did the habit of the nobility visiting the beach. "By the turn of the 19th century the machine could be found on beaches across Europe". It points to period sources that claimed that seawater had health benefits. Fashion and style did their parts (John Nash's Royal Pavilion in Brighton), as did railways. The health benefits were adduced well into the 20th Century; fascist Italy, Nazi Germany, and Spain had beach camps for children's health.

This article is covering an exhibition:

"Tous à la plage!" is showing at the Centre for Architecture and Heritage in Paris until February 12th 2017