You are correct, vi did not use curses as a library.  It was hard coded.

Similarly, termcap started out the same way.   In fact, I know Cornell's fred and I thought a number of other early Unix screen editors like the original Rand e, were hardcoded for specific terminals (I personally put the code for the Lsi and Fox into Fred which was what we mostly had at CMU).   As UCB got more and more different displays, the routines for terminal control also got pulled out and put into a separate library.  Mary Ann eventually became the main person behind it and I'll let her add the details of who did what (I'm under the impression, wnj did the first cut of termlib and then Mary Ann overhauled it).