In this wind sensor, how can I increase the sampling rate (takes up to a minute to update)?
I suspect you're not right about the assumption that this slowness is due to electronic properties of the motor.

On the contrary, I'd assume that the device does relatively low-cutoff filtering in the digital domain, for example simply by averaging several measurements. That way, you don't get a "noisy" jumping speed value, but something that is nicer to read.

On the flip side, you incur group delay, as you notice.

The fact that it rises faster than it falls is probably caused by the desire to be useful for assessing the weather: an average wind of 2 knots with bursts of 20 knots will certainly feel different than an average wind of 4 knots, even if the actual average is the same.