frum people didnt like EMS , so they started Hatzloh
Frum people didnt like Public School so they started the yeshiva system
frum people didnt like the Public bus service so they started their own bus (The B110 bus)
There is no reason a pool cannot be built in Williamsburg for the same reason, besides learning to swim is a HALACHA.
Dont think Giverim in Williamsvburg are strongly urged to put their money in certain charities, there is no reason some of that money cant be used for a pool (The pool could be built in the basement of a Shul or Yeshiva with a seperate entrance)