Sinusoidal liftering in implementations of MFCC
This paper$^1$ suggests:



that the reason is because the filtered versions give less weight to the higher coefficients which provide less discrimination than the lower ones.

That paper references this one$^2$ which shows the plot below indicating how the application of window reduces the variability.



References


K.K. Paliwal "DECORRELATED AND LIFTERED FILTER-BANK ENERGIES FOR ROBUST
SPEECH RECOGNITION"
B.H. Juang, L.R. Rabiner and J.G. Wilpon, "On the use of bandpass liftering in speech recognition", IEEE Trans. Acoust., Speech and Signal Processing Vol. ASSP-35, No. 7, pp. 947-954, July 1987.