Aren't the different views of 'helping yourself' interesting...?
TBH I understand exactly where the OP is coming from. Kids are very different... if I had allowed my two DDs (now 18 and 15) to just help themselves to anything at any time, they would have just been like a herd of locusts, particularly DD1. She can be very greedy at times and eats cos she's bored, cos its there (even if she doesn't really want it!). She will help herself to something and then moan at me cos I let her eat it.
Also I have the house stocked up for nice family meals and I know I would open the fridge and half the ingredients would be gone, if I had let my DDs have free rein in the kitchen.
Granted mine are older now and, of course, they could always have fruit and that type of thing when they wanted. However, I have left a full fruit bowl and when DD1 was younger she has literally eaten the whole lot... just for something to do!
I think they need to understand they should eat when they really need food, not out of boredom so I have always been quite strict on this.
It sounds like the OP's son is just eating out of habit or greed, not cos he is hungry. After all, how can he be hungry after a plate of shepherds pie, veg and a yogurt? TBH I don't think its good to continually eat between meals, although I understand when kids are younger, they need the odd snack as fuel.