I have the same concerns, so I only apply mulch beyond the root line.

I keep mulch on mine year round, my area is considered high desert and it's just too hard to keep my gardens watered otherwise. I move mulch away from the stems as they emerge and the weather gets stable enough but never completely remove it. I put several sheets of newspaper down and just a few inches of mulch over, does okay for weeds but still have to pull some. I'm slowly transitioning to just using pine straw since it doesn't pack down as tightly as wood mulch.

I think it is winter when they peonies need to be the right depth so they feel cold. If you want to be safe maybe thin out the mulch in the winter when weeds are not as much a problem? I kept a thin layer of mulch over mine all year long and it does not seem to have affected bloom.