People are typically okay with site owners having their IP, because site owners tend to not be malicious. You could only connect with people that you completely trust, but with many applications the users might be complete strangers or merely internet acquaintances. Given the power, there would be malicious users taking advantage of it. This was a big deal with Skype because people weren't aware that adding a contact could reveal their IP to that person, and/or were not aware that revealing their IP could lead to DDOS attacks or other forms of abuse/stalking.

If you want this behavior, you have to use WebSockets.

WebRTC is peer-2-peer.

Yes, it's a tradeoff.