Wrong. That actually is one of the standards that can be broadcast, although I suspect it most cases 3:2 pulldown will be used to broadcast at 59.94 fps. But the reason that is typically done is because switching a broadcast stream between the different frame rates can cause problems for some TV receivers (or at least this was the case early on), therefore it is safest just to run everything at the same frame rate.Television stations and associated cable networks can't air 23.98fpm.
But 23.98, 29.97, and 59.94 fps are all valid per the ATSC broadcast standard.