DCT step in MFCC process
DCT is not used only for going back to time domain, it is also used due to it's "de-correlating properties". By saying that I mean compression of most of the information in smaller number of coefficients. Although in theory we could use the DCT to calculate the spectrum, but I never saw anyone doing that. Usually thing is simple:


want to analyse the spectrum? Use DFT
want to compress and de-correlate data? Use some flavour of DCT


Also one very important thing. In case of DCT, the equivalence property of convolution and multiplication in frequency domain doesn't hold:
$$x[n]\star y[n] \nLeftrightarrow X_{DCT}[k]\cdot Y_{DCT}[k] $$
which is the fundamental property (homomorphic) used when calculating the MFCC's. It allows to perform the Cepstral Mean Normalization and remove the "convolutional distortions", such as vocal tract. For more info please refer to my previous answer.