I don't think there's any other way to get a ValueError out of min/max, but I haven't actually looked at the code to check.  Of course, if we want people to rely on that, we'd need to document it.

'next's default is used to return a sentinel when the list is exhausted, not when it would otherwise raise a ValueError.  It is a somewhat related case, but is not exactly parallel.  The sentinel for next indicates the end of an ongoing process.  The proposed argument to min/max would *replace* an error with a sentinel value.