My elementary school music teacher was very schoolmarmish and prim -- almost like Ana Gasteyer's Bobbi Mohan-Culp character -- and had training in opera performance. She also did the "ta"/"titi" thing, but backwards. She would, for example, teach us a ta/titi sequence -- writing the notes on the board, teaching us the names and shapes of the notes, having us sing/perform it several times -- and only then reveal the lyrics to be "Baa Baa Black Sheep, have you any wool?" Her years of musical training taught her that getting the details right early on was super important. I'm incredibly thankful for having had teachers like this.

It sounds like the teachers you've had who said "just do what makes sense" have punted on the act of teaching itself. They either don't know how to, or are unwilling to, do the hard work of providing detailed instruction and holding kids to a high standard of learning. That's just sad to see man.