People complained about not having a Reno counter for years. Now that we finally get it, people are losing their minds.
The problem isn't a reno counter. That's fine, that's what the card is intended to do. It's when priests shuffles 20 copies of that stupid bird in my deck that triggers me. Ruins the fun.
Make it a Battlecry, problem solved
Changing to battlecry actually makes it worse. Rogues would be able to abuse it with Shadowstep. Shaman would be able to abuse it through Corrupt the Waters. And there's Brann Bronzebeard in wild. Way less birds, but easier to abuse in other classes.