Ctrl-C in Emacs is not "terminate program", it is "start of user command", in most modes. Similarly, even in vi/vim, Ctrl-C does something completely different. So this has nothing to do with the terminal whatsoever.

It's an even more basic Unix affordance, that terminals had a key-binding that generated the interrupt signal, and programs could define useful behaviors that commenced upon receipt of interrupt.

It made sense that interrupt in Emacs could get into a controlled state of receiving the next command. It's a little bit like the SAK (secure attention key) concept, as seen with Windows use of ctrl-alt-del.

Edit: Ironically, as a long-term emacs user, I don't really remember any commands that start with ctrl-c! For me, the most common sequences start with ctrl-X or meta-X. Or the prefix search commands ctrl-S and ctrl-R.