I like to use Priest aggressively to kill tokens or reset cards like Chasm Skulker/Rockslide Elemental so that you don't have to constantly worry about what's under it. If you do take out a big nasty, though, Gods Willing has your back. I even play Priest on empty board just to keep up the pressure or trigger Mentor, he's not just a removal spell.
I use the Priest to also target in a similar fashion and believe I've eluded to a few of the same points made here. As an example, if that's the only option I have, I will play priest into an empty board but as I said above, it feels awful doing so (and would rather it be a better card for this decks purpose - I believe this was something you mentioned before - when I'm holding it, would I rather this be a different card. It's that specific analogy that lead me to the suggestion of reducing 1).
The comment that 'he's not just a removal spell' is the point I want to mention. If we use any card in any deck solely for the purpose it was put in for (unless the card is narrow and only has that one function), than we lose versatility/flexibility. We constantly have to change/adapt to our opponent, their deck archetype, game state, board state etc and the more we do, the more chances we have to be successful. In doing so you can change the value of a card based on the way you play it. Having said that, the purpose to include Priest in the first place is a removal spell and that's where it gains its most value. Given a hand with choices, I'd assume we'd both be holding the priest for a target and playing other options to the board. Then playing priest when he gains that value. I hope I haven't come across as saying that's the only value it has or implied that's the only way I'm using him. It's just his best use.
I get that you include 3 of them to improve the frequency in which you see 1 of them but it's the games where they keep showing up that become the basis for my suggested change. Back to your in hand test and the number of spins I've had with this deck, there are enough cases that came up where I was 'boy I wish this was X card instead of Banisher Priest'.
elk