You could do that, but we like to separate C programs into separate translation units, chiefly because:
It speeds up builds. You only need to rebuild the files that have changed, and those can be linked with other compiled files to form the final program.
The C standard library consists of pre-compiled components. Would you really want to have to recompile all that?
It's easier to collaborate with other programmers if the code base is split up into different files.