When I look at a Hertzsprung-Russell diagram, I'm able to see a main-sequence line from the most luminous main-sequence stars at the top left to the dimmest main-sequence stars at the bottom right. However, this line isn't straight - it's quite squiggly. Why is the line squiggly, and not defined by a polynomial or rational function?
Here is another plot of a Hertzsprung Russell diagram (luminosity versus temperature), but this time based on theoretical models. (The plot is from D. Prialnik 2000, An Introduction to the theory of stellar structure and evolution). Note that the zero age main sequence is well behaved in this plot. Luminosity and temperature are related by smoothly changing power laws that are largely due to the varying temperature dependence of energy generation and modes of energy transport within stars of different mass.
Your diagram is actually an absolute magnitude versus colour diagram. This is not the same thing. The transformation between absolute magnitude and luminosity and especially between colour and temperature are distinctly non-linear and dependent on what particular spectral features happen to be present in the photometric bands that are used to construct the plot. For example, there is a knee for cool M-dwarfs because the B-V colour "saturates" at a value of about 1.6 because there is hardly any flux in the B and V bands and their ratio doesn't change very much with temperature because of the characteristics of the opacity sources in the atmospheres of these stars at those wavelengths.
To demonstrate that the plot is not necessarily "wiggly", the plot below shows the colour-magnitude for the Hyades and Praesepe clusters (basically at the ZAMS) in the Gaia filter system (from Babusiaux et al. 2018). Nice and smooth - though it doesn't cover as big a luminosity range as the Hipparcos plot in your question; the main wiggle at B-V~0.3 is still in the Gaia data (off the top of the plot), but the M-dwarf "knee" is smoothed out by the redder filter response.