In SunOS 4.x `FILE` was not opaque, and `int fileno(FILE *)` was a macro, not a funciton, and the field of the struct that held the fd number was a `char`. Yeah, that sucked for ages, especially since it bled into the Solaris 2.x 32-bit ABI.
It was a then-important optimization to do the most common operations with macros since calling a function for every getc()/putc() would have slowed I/O down too much.
That's why there is also fgetc()/fputc() -- they're the same as getc()/putc() but they're always defined as functions so calling them generated less code at the callsite at the expense of always requiring a function call. A classic speed-vs-space tradeoff.
But, yeah, it was a mistake that it originally used a "char" to store the file descriptor. Back then it was typical to limit processes to 20 open files ( https://github.com/dspinellis/unix-history-repo/blob/Researc... ) so a "char" I'm sure felt like plenty.