I got it from this video, which attributes it to Quintilian: https://www.youtube.com/watch?v=_enn7NIo-S0

And I seem to have swapped 'c' and 'k'; Quintilian wished to eliminate 'k' in favor of 'c', which is probably why you think there is no Latin letter 'k'.

If you look at the qualifier Quintilian adds (the video translates it as "the letter C keeps its strength before all the vowels"), you can see why K was in use at the time -- the sound change familiar from modern Romance languages, where C "softens" to [s] or [tʃ] before front vowels, made indicating [k] before front vowels difficult.

That is an innovation to deal with language change. It is not a part of classical or old Latin. Quintilian isn't proposing dropping K because C makes it unnecessary; he's proposing retroactively not adopting K in the first place because the change that prompted people to use it is wrong.