The benefits and limitations inherent to the 2D post-processing of measurements from Brillouin optical time-domain analyzers are investigated from a fundamental point of view. In a preliminary step, the impact of curve fitting on the precision of the estimated Brillouin frequency shift is analyzed, enabling a fair comparison between the representative noise reduction algorithms studied in this paper. The performances in terms of signal-to-noise ratio, experimental uncertainty σB on the Brillouin frequency shift and spatial resolution delivered by advanced image processing methods - such as wavelet transform and non-local means algorithms - are then compared with the impact of a 2D Gaussian filter. The major discrepancies observed when comparing the gain in signal-to-noise ratio to the σB reduction are then determined by exploiting the separability of the Gaussian filter, which reveals that noise reduction is only effective along one dimension of the 2D array of measurements and originates from a digital reduction of the system analog bandwidth. The signal-to-noise ratio improvement obtained from filtering in the spectral dimension is only illusory, since its action is redundant with the curve fitting procedure to estimate the Brillouin frequency shift. Finally, the maximum σB reduction achievable by digital post-processing is theoretically given, hence setting a fundamental limit to the improvement brought by data processing.