Mel filter in MFCC - is it necessary?
Mel filter bank is important due to following reasons:


It applies the Mel-frequency scaling, which is perceptual scale that helps to simulate the way human ear works. It corresponds to better resolution at low frequencies and less at high.
Using the triangular filter-bank helps to capture the energy at each critical band and gives a rough approximation of the spectrum shape, as well as smooths the harmonic structure. In theory you could manipulate on raw DFT bins, but then you are not reducing the dimensionality of your features - this is the whole point of doing filter-bank analysis, to capture the spectral envelope.


Obviously warping of frequency scale can be altered. Other mappings are possible, such as Bark, linear, etc. Mel is just one out of many options. To finalize, you can always calculate more filter-banks to have coarser scale (getting closer to actual DFT), but you will notice that at some point it will degrade the performance and your features do not carry essential information.