I would be ok with the equivalent of the "fi" ligature, where two letters would be drawn slightly differently when next to each other.

Why? Monospaced characters fit in their separate cells.

If the ligature takes up the same horizontal space as the characters it represents, then I don't see why not.

hard disagree. i use monospace fonts with ligatures for programming. primarily i get things like -> rendered as a full arrow or == connected or ... as an actual ellipsis. it's subtle but it's nice.

I've also seen nice use of ligature for markdown formatting.

the idea that ligatures shouldn't be used with monospace fonts would also break monospace in multiple languages as some languages require ligatures to display single characters correctly.