I have the same problem on catholiclibrary.org, but insist on having something as the book date for every work. My solution is to temporarily default to the author dates until the book date can be refined. If there is no known author date I at least have a date range, hopefully to century or better.

Author dates are a much smaller data set, can be generally supplemented from public marc records (viaf, loc, etc - I don't do that, but it's an option) and at least provide basic filtering / sorting.