What is the most precise frequency analysis spectrography algorythm?
You don't have a loss in time precision when using FFTs because the FFT is fast. The FFT is just a fast algorithm for implementing the discrete Fourier transform (DFT), nothing more. Instead, there is an inherent tradeoff in time and frequency resolution due to the Heisenberg uncertainty principle. While its statement is explicitly focused at quantum mechanics, the same underlying principle remains true: the more precisely you know the frequency of a signal, the less able you are to localize it in time.

With that said, there are another class of techniques known as bilinear time-frequency distributions that are appropriate for some applications. One example is the Wigner-Ville distribution. In short, these techniques can provide simultaneously high resolution in time and frequency. The cost, however, is the presence of spurious features in their resulting outputs. There do exist modified versions of these distributions that can reduce the magnitude of the artifacts, however.