I like the secret alternate style of play you included by giving the player a free upgrade, reroll chance and +2 health by playing through levels without collecting coins. However it is WAY too hard to navigate the levels without accidentally collecting a coin.
I'm trying to beat 9 levels coinless and I will always end up running into sections where there is a coin located just below a drop, or in the way of a passageway. Level six onward I just collect coins normally because I'll scan the map before I start and realize I'm going to have to collect a coin to proceed.