Panerai Ferrari Chronograph replacement buttons?

Repair centers do this because usually when you lose a crown or pusher there has been an opportunity for water or dirt to get inside the movement. In years past a repair center would replace a crown or pusher alone, then the watch would be back a month later not working, and the client would blame the repair center saying 'it was working before you replaced the part'. Another possibility is that the watch lost the crown or pusher because of a strong impact, so that's another reason why they don't offer just to replace the part without checking the movement.

I can't say if your watch had either of those problems, just wanted to give you the point of view from the other side.

 

Panerai, being part of the Richemont Group, won't sell parts to independent watchmakers unless they have a parts account. In order to get a parts account in the US, you need to be a certified master watchmaker and have a repair shop with a specified amount of space, tools, and equipment. This is common practice these days among watch brands.