My driver's license information is taken by plenty of businesses. My passport is photocopied in most hotels outside the US, certainly in "privacy-conscious" Europe (US hotels generally do not make copies or scans of IDs). Given that this information is already out there and liable to theft or misuse anyway, I don't see what the difference is in sending it to one more business. Frankly, sending the data in secured form over the internet seems much safer than having a photocopy of my passport sitting in the desk drawer of a random hotel where any employee (or friend of an employee) can access it.
I do not have a FB account, in part because I view its operations as a much greater invasion of privacy, even though FB doesn't ask for driver's license information. With FB, everyone else on the service--plus advertisers--knows way too much about you.