I can't run C on a 8-bit calculator either. At least not using GCC or Clang or any other mainstream compiler. Sure, I could use some toy compiler for that, but then 99% of the libraries I'd like to use won't work there anyways, due to a variety of issues.
I was about to object, but actually it looks like you're right; tigcc appears to only target the TI-89 et al. which run on the 16-bit Motorola 68000 series. A quick search doesn't give me any C compiler for the TI-84 after all.
Your actual point, of course, is valid regardless:)