Counter-counterpoint: using 2 bytes to signal one relevant operation creates ambiguity out of thin air. If all you care about is "where does the line end?", having CRLF as a line ending creates edge cases for "there is only CR" and "there is only LF". Are those line endings or not? How do you deal with them? And what's LFCR?
Personally speaking, I've always written my parsers to be permissive and accept either CR¹, LF, or CRLF as line endings. And it always meant keeping a little extra boolean for "previous byte was CR" to ignore the LF to not turn CRLF into 2 line endings.
¹ CR-only was used on some ancient (m68k era?) Macintosh computers I believe.
P.S.: LFCR is 2 line endings in my parsers :D