If you were sharing the doc via another service that required a login (and pretty much anything that doesn't post it to a public URL is going to), wouldn't you hit the same problem? It's hard to do collaboration (even if it's read-only collaboration) without identities.

Overall, it seems to me it's probably both more likely than a random family member will have a Google account, and/or be willing to sign up for one, than sign up for a different service that's less well-known and has fewer services based on that login.