OFDM channel estimation
If some values in $X[k]$ are zero, you cannot determine the impulse response of the complete channel bandwidth ($-f_\mathrm s / 2 \ldots f_\mathrm s / 2$, with sampling frequency $f_\mathrm s$). The IFFT of the estimated $\hat H[k]$ is rather a low pass filtered version of the channel. This might or might not be what you want.

In reality, you can never measure the complete bandwidth of a channel, as it is virtually infinitely large. For a communication system it is usually sufficient to know the channel transfer function of the band in which you intend to transmit a signal. If you transmit only on a fraction of subcarriers of an OFDM system you're effectively narrowing the transmission band and you might be satisfied with knowing the impulse response of this narrower band.