`bat` is definitely a `cat` replacement as it has the essential functionality of concatenating files. The automatic paging is only for printing to standard output and it doesn't meddle with this functionality.
By the way, zsh built-in pager (invoked with `<`) has this behavior. It prints output to display but it pipes it to an actual pager if size is large.
Googling that i get:
cw - sound characters as Morse code on the soundcard or console speaker.
Must be a pretty obscure replacement when all the google results are for a different unix program. Unless im missing the joke.
As an aside, bat really sounds like its replacing less not cat.