The taxis do indeed still run to/from the major beaches though the prices have increased - the 2024 price to Trunk Bay is $12/person.
That said, I second
@daviator's comments. A car with 4 wheel drive is somewhere between useful and necessary to visit the east side of St John and I heartily recommend doing so for a day or three while you are at WSJ. But there is no need for get one for your entire stay - taxis are ubiquitous and reasonably priced as long as you are a party of 4 or less.
View attachment 95975