This design makes so much sense with the flap guarding the nozzles....I just got one that does not have this feature (nor does it have self cleaning), and I'm afraid of what cleaning it is going to be like.
No it doesn't get damaged when you sit on it. The way they built it is for the toilet seat to sit on top. I do wish the nozzles were a tiny bit further out from the back of the toilet. But I have no complaints with it it works well.