It's not a broken implementation of readline, it's either a failure to use readline or improperly set terminfo. TTYs in canonical mode will support backspacing, but not moving around inside text. "Ctrl-Left go back a word on my laptop, but when I ssh into my server, it just prints some weird characters?" reaks of straight up canonical mode.

And say you had this problem, guess what is not going to work? "I have a problem with my command window", "I have a problem with my console", "I have a problem with my TTY".

This is why vocabulary is important.