Compensate for phase shift of Hilbert transform
1) A Hilbert transform has a very very long impulse response (above some given noise floor), so you need a ton more data to manufacture an analytic signal, otherwise you won't have enough to span the width of the Hilbert impulse response filter without serious edge truncation effects.

2) Instantaneous frequency estimates from this type of artificially approximated analytic signal can be very noisy, so often has to be low pass filtered to significantly below half your sample rate.