The reason I would want to do this is to support very old browsers (e.g. IE 6) that does not implement the more secure Digest method. If all new clients advertise the types of authentication they support in the HTTP protocol, this should be doable in principle. If a client does not advertise that, Apache should fall back to the Basic auth scheme.
The advantage over using Basic auth is apparent: it would prevent passwords to travel in clear over the network most of the times, since the new browser are the majority, while still supporting some very old browsers that are still around. In other words, it would increase security.