The carriage return is moving the typehead to the beginning of the line, not starting a new one.

Line feed is the command that is incrementing to the new line.

Those two commands almost always run together so it quickly became possible to invoke with a single CRLF command (in ancient computer times)

I know, and the Return key both returns the carriage and feeds the paper forward a line on teletypes. Hence the symbol ⏎, indicating "down and to the left" (for LTR languages.)