We don't need to get terribly cerebral to note the basic mechanism of proportion, whereby $10 added to the daily food cost of a person who makes $50/day is vastly more impactful than the same $10 added to the daily food cost of a person who makes $500/day.
Also these numbers are super weird. It's probably more like $10 total daily food cost going up to like $10.30, and going from making $30/day (part time minimum wage) to $50 (near full-time minimum wage).
I'm not seeing a great deal of causation in your theory. The same amount of food is being produced, thus the same amount of work is done - so extra employees are not required. If anything, in your closed system theory, the food producer is going to laugh and pocket extra profits.
https://www.nzherald.co.nz/business/the-conversation-inflati...
Show me which countries have wage growth for lower socioeconomic demographics currently matching or outpacing CPI? It is not happening.
Scale that up by a factor of millions across the country, and you've closed the income gap. That's the power of inflation.