President as a British reminder of a captured American frigate

Did the capture of USS President and British copying of the frigate explain why her name was never reused?

British reuse of President is explained as a deliberate reminder of the captured American frigate.

The British continuation of President kept the captured American frigate's name in use. It is described as a way to remind American counterparts of the capture. An unrelated explanation involving the president of the Board of Trade is explicitly rejected. The question's claim that the name was never reused remains distinct from the British naming practice discussed in the reply.