Puerto Rico does not want to be "given up". It wants, and deserves, statehood. A so-called "independent" Puerto Rico would be nothing more than an impoverished client of the United States.
> Taiwan deserves provincehood so it isn't a impoverished client of the PRC.
Now, Taiwan is quite rich, but still, optics matter. Better to give Puerto Rico tons of reparations if you are worried about it being impoverished and dependent.