Look at it this way.
We have BM, you can always play BM because it only requires cards that are available every turn.
BM is a rather bad and vulnerable strategy, so we can add some cards that help get our biggest treasure cards in play more often, like a sifter such as Warehouse. But if we add too many Warehouses and not enough money, we start feeling like a village idiot. And because Warehouse is non-terminal, we can add other terminal cards. Hey, look at that Taxman that we can now play every 2 or 3 turns! And maybe we can include a card which gives us a +Buy, such as Pawn.
At which point does this stop being BM and become and engine?
That's the point I was trying to make. In games with no virtual coin or cost-reduction (or cheeky gainers like HoP), the only thing you can use to buy stuff is actual Treasure cards. And not every strategy which has to use Treasure cards can be turned into a super engine, simply because it lacks a few key cards. But that doesn't mean you're only allowed to buy Treasure cards or VP cards. You can keep adding helpful cards to a point where it's neither BM nor a full fledged engine.
I reckon that there are enough kingdoms where playing such a strategy is the best option and that there are enough of those kingdoms where Taxman is a viable card.
They are neither slogs, nor rushes, just regular Province games where you can shave a few turns off the default 4 Province for BM average (was it 17 turns?) by incorporating enough other useful cards.