Why does more bandwidth mean higher bit rate in digital transmission?
It's a subtle point, but your thinking is going astray when you think of a 330-Hz tone as somehow conveying 660 bits/second of information. It doesn't &mdash; and in fact, a pure tone conveys no information at all other than its presence or absence.

In order transmit information through a channel, you need to be able to specify an arbitrary sequence of signaling states that are to be transmitted, and &mdash; this is the key point &mdash; be able to distinguish those states at the other end.

With your 30-330 Hz channel, you can specify 660 states per second, but it will turn out that 9% of those state sequences will violate the bandwidth limitations of the channel and will be indistinguishable from other state sequences at the far end, so you can't use them. This is why the information bandwidth turns out to be 600 b/s.