S.gfx is right. Except that anyone who has a gmail account actually has a Blogger account - most of them just don't know it.
I'm not sure if any product will be able to give Kit what s/he's looking for though: the aim is to let anyone log on using the existing email account details (name and password) that they have. This would mean that the blogging platform would have to authenticate visitors via ANY existing email provider, be it yahoo.com, mybusiness.net or obscureISPinOuterMongolia.mo
I think (but am not 100% sure) that this would be a pretty big ask.
(To explain my thinking here: In the Blogger Help Forums, there are regular help-requests from confused folks who have Google accounts that use other email names (eg firstname.lastname@example.org) - and it's a struggle to get them to understand that their Google account name just happens to look like their email address, and that their Google password doesn't automatically stay in synch with their email-account password.)
I don't understand OpenID enough to know if it's the sort of thing that gets around this - meaning that the original question could be phrases as "is there a Blogging platform that allows blog membership via OpenID". But it may be.