The reason for avionics off during engine start is because the starter motor generates powerful spikes, going up to a few hundred volts, for a few milliseconds.
There is even an ISO spec with the pulse shape which the [automotive] product has to withstand. It's not a problem to design to the spec. Needless to say, avionics designers have never seen this, and have no reason to, because the starter motors used in planes are totally different to ones in motor vehicles (actually they are identical)
Historically, most avionics would get blown up by the spike, though not always and perhaps not the first time.
The spike also gets coupled (inductively and capacitively) into nearby cabling and could get into avionics through onforeseen channels (if the wiring is badly routed).
A lot of seasoned pilots regularly going to big airports use a handheld radio to do the departure clearance and engine start calls, so they don't waste avgas.