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Because the error amplifier is an opamp integrator, which has capacitive connection in the feedback path...and capacitor is super high Z at low frequency, and hence the error amplifier has super high gain at low frequency.

High gain at low freq means accurate vout at low freq......to know this it helps to know about ideal opamp theory, and how they have super high gain in ideal world, and if you go through derivation of the Vout/Vin = -Rf/Rin for an inverting amp then you will realise why a high gain gives you accurate vout.

..Remember the ideal GND?....remember that the + and - inputs of an opamp with neg feedback are the same...but not exactly the same....if gain is low then they are further apart.....etc etc..

...it may still overshoot...it depends

Well yes you need to know if it is voltage mode or currnt mode...and you need to know the current sense threshold  voltage....and if the error signal is divided down b4 going into the pwm comparator........ then you need to know that so  that you can incorporate it into bode plot calcs.