Aside from some a couple performance critical parts of code or if you're trying to push the hardware to it's maximum limits with effects or complex mechanics, C is totally sufficient for writing entire (and performant) games on the Game Boy. Many polished homebrew GB games have been (and are being) written and completed using C.
Of course, now the number of games now being made with GB Studio completely eclipses the number written in C and assembly.
Most of the GBDK/GBDK-2020 API used for C development is written in assembly, so if you use C you get some benefits of using assembly anyway.