Who should pay? Mechanic broke piece

If I had been the one working on your car and that piece broke/cracked/chipped during the “normal course of a routine repair” I would have replaced the part and added it to your bill (no labor charge, of course). As cars age, sometimes we can follow repair procedures to the letter and still have plastic pieces brake due to the normal deterioration of materials. Now if I took your door trim off and accidentally stepped on it, I’d replace it for free.

I assume you have some level of trust with this shop, and believe them that they didn’t break it through carelessness.