Continuous? This is a mathematical concept. If this applies to physical reality is already subject to discussion.
Sampling at infinite precision? You are making up your argument. You nerve cells can hardly sample at infinite precision.
AFAIK nervous cells do not frequency modulate. They have varying recovery times though.
However the bandwidth question is not decided by how hard it would be to emulate nerve cells and how much bandwidth this would need. We are discussing the bandwidth that could be pushed into a human's input channels. I doubt that this would be more than 10 Mbit/s (= vanilla ethernet). Let alone the >100MByte/s my Sata Drives can sustain. --> nothing ultra high bandwidth here.
Basically you argue that analog has "data rate" due to the fact that you would need unlimited data to faithfully reproduce everything down to the noise floor of an analog signal. With the same argument you could show that every (digital) signal exceeds its own bandwidth.