My concerns not about the bad reviews, it's about your personal privacy. I think the reply posted by Pual gives many good example.
Besides, Airbnb is a tool that can connect people in real world, it could bring real connection within people. It is not a comforable to share too much details with new friends (like your new host). For example, I book the room and stay there one day or two, I do not want the host welcome my by "Hi Man, how's the trip in XXX last Chrismas, I saw the host mentioned you traveled with a beautiful girl, why didn't she come with you this time?".
What I want is not totally block the reviews, the reviews do help travler to avoid some wired guys and bring punishment to the host/traveler who hurt others.
But the content should be controled, like
1. The time could be "this month", "last month", "this year", "last year" ... , this is good enough to show how the host/traveler behaved measured by time.
2. User should have the ability to hide some reviews which expose too much details he/she don't like. But Airbnb could show a label like "this review is hidden by this user". Even more, let user could explain why he/she hide it. If a host hide 90% of his review, I won't chose that. Same logic for traveler.
3. We already has a rating system for host, if we need, we should build a similar system for traveler. If possible, we could do questionnaire based review, limited contents the host could write down. So the host only could say "Yes/No" to "Did this traveler maintain a clean room?", instead of all details of what you eat, how you eat, how many you eat and how many you left on the floor.