Most of are guests are domestic, and like most Americans, I doubt they all have passports, so requiring copies of their passport would be impractical. Also, getting copies of DL seems illogical, too. We get 5-10 guests per week, so running making copies of DLs and PPs would seriously hinder the check-in process.
Instead, and call me naive, we trust in the Airbnb process of verifying guests' identities. Over 320 reservations, and easily over 400 guests, we haven't had any problems requiring their use of their IDs.
Anyone looking to book and/or trabsact offline we categorically decline and report to Airbnb immediately.