I think that this is something of a problem for an institution that faces a continual struggle to remain relevant to modern Britain. If the Royal Family are flesh and blood like all of their subjects, there's no way on earth that they could resist Frazzles, Chipsticks or Wotsits. Their continual failure to do so seems to me to be a tacit admission on their part that they are different from, superior to, their subjects.
From the point of view of transparency, I should point out at this stage that I have no data to prove my thesis, only what I have observed and deduced. Here's a list of the key Royals with the snack foods I can honestly imagine them having ever eaten.
HRH Queen Elizabeth II
Mini-poppadums. Ready salted Kettle Chips.
HRH The Duke of Edinburgh
Petit Mignons, onion flavour. But he didn't enjoy them.
HRH The Prince of Wales
HRH The Duchess of Cornwall
HRH The Duke of Cambridge
HRH The Duchess of Cambridge
HRH Prince Harry of Wales
The hero of the clan. All flavours of Walkers and Golden Wonder crisps, including any special charity edition flavours. Mini-poppadums. Chilli rice crackers. Monster Munch (all flavours). Space Invaders. Scampi Fries. Frazzles. Chipsticks. Wheat Crunchies (all flavours). Pringles. Square crisps. Discos. Tubes. Mini-Cheddars.
HRH The Duke of York
HRH The Earl of Wessex
I'm not a republican. But I feel that if the Royals continue to scorn us with their stand-offish refusal to eat crisps I probably will become one.