I would be remiss if I did not point out that calling said program cat is a misnomer. Instead of 'string together in a series' (the actual dictionary definition, which coincidentally, pipes actually do) it quickly became 'print whatever I type to the screen.'
Of course, the example @arendtio uses is correct, because they obviously care about such things.
Having separate commands for outputting the content of a single file and several files would, however, be an orthogonality violation. YMMV whether having a more descriptive name for the most common use of cat would be worth the drawback.
It would fit in the broader methodology of 'single purpose tools that do their job well' or 'small pieces, loosely joined', but yes, probably too annoying to bother with.
Of course, the example @arendtio uses is correct, because they obviously care about such things.