Seems fine to me to think of the turn in whatever number of phases you want, so long as you mentally convert whenever the card text refers to a particular phase. It's occurred to me that not only are there is there this hidden "draw" phase but two others as well. Broken down more completely, I'd say your turn consists of actually six distinct activities:
Action Phase:
(1) Process duration cards and Horse Traders cards still in play from previous turns.
(2) Play and resolve action cards from your hand.
Buy Phase:
(3) Play and resolve treasure cards from your hand.
(4) Buy cards from the supply piles.
Cleanup Phase:
(5) Discard cards in play, performing clean-up actions as needed.
(6) Draw your next hand.
Making the mental delineation between steps (3) and (4), rather than lumping them together into "the Buy phase" helps understand one of the rules of Dominion better, which is that you have to play all treasures you're ever going to play that turn before you buy that first card. So you can't lay down two Golds, buy a Grand Market, then plunk down some Coppers for a second buy. Admittedly it's not often where that distinction actually matters, and Grand Market is probably not one of the cards you use to teach newcomers to the game. But strictly speaking, steps (3) and (4) are very different activities performed at distinct, non-overlapping stages of your turn. So I think it's perfectly fair to make a separation between them, just as you've pointed out for steps (5) and (6).