Why aren't headphone jack shaped plugs used for data?
Digital signals are highly susceptible to the noise generated by rotating the plug. 

For audio, these noises (cracks) are rarely audible unless they last longer than 50us (simply because of the fact that we're unable to hear frequencies over 20kHz). So, the cracks becomes audible only when the surface of the connector has deteriorated enough that the period of lack of connection is substantially longer. 

As a rule of thumb, any connector where there are moving parts while the connection is established, is a terrible idea for high frequency digital data. It might be acceptable for low frequency digital data, as well as power supplies.

Finally, most digital standards require quick detection of the disconnect - even though the above issue could be worked around with proper ECC (Error Correcting Codes), USB assumes that any loss of connectivity for over 2ms is considered a disconnect. (USB 3.0 SS is even more strict).