I do re-use my clay pots if they are in good shape, Bree. Scrub 'em off and soak in a little bleach/water then let them dry in the sun. But they are pretty cheap to buy here, so I keep a couple of new ones around, too.
Sometimes I've had to break a clay pot to get the orchid out, and if the roots are stuck to the clay, I leave clay pieces that are held by the roots and just pot them up as part of the new medium.
Clay does dry out a terrestrial plant with soil in the pot more quickly than plastic because of wicking action, but not with orchid bark mix. Plus the clay itself holds and releases water gradually which keeps the roots cool. In hot, dry weather I go around and spray all the clay pots to keep them damp and cool.
All my orchids that like it cooler are in clay pots - the Phals and Cyms especially like them. For the rest I am gravitating towards wood baskets, with coco fiber in them.
Your Paph really is lovely, and 3 flowers open at once, what a treat! Here's my Bl. 'maybe Yellow Bird' with a new flower. It's a richer color than the 'Yellow Bird' that has a tag. Maybe one's getting more water than the other.
