Diode has varying characteristics based on the operating point (i.e. how hard it's being driven, ambient temps, etc..).
In practice, the driving signal is plenty, there's no concern about snr or too low signal levels - you just need good filtering in order to get rid of all unwanted components.
it's quite unusual to make a perfect matching network for a simple diode multiplier, as it doesn't provide any practical benefit, and severely restricts the operating conditions of the multiplier to a very certain input signal level.