> Why does the fi ligature even have its own code point? No idea.
On of the principles of Unicode is round trip compatibility. That is you should be able to read in a file encoded with some obsolete coding system and write it out again properly. Maybe frob it a bit with your unicode-based tools first. This is a good principle, though less useful today.
So the fi ligature was in a legacy encoding system and thus must be in Unicode. That's also why things like digits with a circle around them exist: they were in some old Japanese character set. Nowadays we might compose them with some zwj or even just leave them to some higher level formatting (my preference).