The biological foundation for MFCCs are pretty weak. The mel-scale, which the mel-spectrogram and thus MFCC uses, is a rough approximation of how frequency differences are perceived along the frequency axis. The log transform of amplitudes is better than linear, but not really a good model of the ears loudness perception - which is non-uniform both with amplitude and frequency, as well as state-dependent (temporal masking).
The choice of hop-lengh is also maybe roughly close to what the human ear has, but vastly simplified - the ear temporal resolution is not uniform either. And no binaural representation either, a critical part of the human auditory system.
The primary reason for using MFCCs is its numerical convenience. The log mel-spectrogram (when computed with appropriate parameters) preserves a large amount of the information in an audio signal - but reduces the feature space considerably and introduces useful structure (time-frequency). Using a 32 ms hop, 512 samples at 16kHz = 32 frames per second, and 64 mel bands one can reduce one second of audio from 16000 dimensions to 64x32=2048. Then when computing the DCT-II to get the MFCC, most of the energy of this ends up in the lower coefficients. This lets us drop the higher coefficients without loosing much information. Typical would be 20 (or 13) coefficients, leading to 20x32=640 dimensions. The information in the different coefficients also tends to be much less correlated than the input spectrogram, an advantage for some models - such as the commonly used GMM-HMM (Gaussian Mixture Model, Hidden Markov Model).
Bottom line is that the feature space with 640 MFCCs per second, instead of 16000 samples per second, is much easier to learn. This dimensional reduction and feature transformations of MFCC is very useful, even if the input is not speech. So one can make OK performing systems for many non-speech tasks using MFCC.
That said with the advent of deep learning and larger amounts of data and compute - MFCC based models are being outperformed by log mel-spectrograms processed by 2d Convolutional Neural Networks, as well as raw waveforms processed by 1d CNNs.
Note also that in the majority of cases, we are still struggling to achieve human level performance. And with supervised learning, our labels are typically provided by humans - a performance roof which the model cannot easily surpass. In this scenario it is not that problematic that our audio reception is limited by loose inspirations from the human auditory system.
There are notable exceptions though, such as ultrasound (for bat detection etc) and infrasound (for condition monitoring) - there it is critical to go beyond the frequency range that human hearing has.