One use for CR without LF was to overstrike passwords on printing terminals. You'd enter your password (which would appear on the paper) then the system would go through several rounds of issuing a CR followed by overstriking the password with random characters.
I still use CR without LF all the time. If I'm writing something that features a long loop, I might want status updates, so printf("%d \r", percentage); helps tremendously. You'll need to fflush(stdout) too, since usually flush is triggered by "\n".
On the other hand, there are far fewer use cases for LF without CR, certainly nothing that isn't better done using ANSI codes.
This the use of CR without LF on a virtual TTY. On a real TTY or typewriter there is less use, but as one user pointed out one could remove information like a password which was printed.
LF without CR is something that one would do on a typewriter for typing tabulated data or mathematical formulae. It's just a way to go "down" but stay at the horizontal position you were previously at.
