I think it's largely for historical reasons.
A Unix file descriptor is a small
int value, returned by functions like
creat, and passed to
close, and so forth.
At least in early versions of Unix, a file descriptor was simply an index into a fixed-size per-process array of structures, where each structure contains information about an open file. If I recall correctly, some early systems limited the size of this table to 20 or so.
More modern systems have higher limits, but have kept the same general scheme, largely out of inertia.