My experience has been that whole foods are much cheaper than processed foods, and don't take much longer to prepare, especially for simple meals.
Budget carnivore (cream/butter, ground beef, eggs) I think can be done for under $10/day, and premium carnivore (eg grass-fed steak, pasture-raised eggs, wild salmon) costs me $20-30 per day as a 200+ pound adult male. Normal diet with snacks cost me something similar in the past.
I think you could probably construct a healthy-ish diet for under $5/day (eg cheap calories from olive oil & starches, cheap protein from factory chicken, pork & eggs, also mussels; if you're eating plants for VitC you could go into protein sources like canned sardines or tuna)
I think the idea that whole foods are expensive and cooking is difficult and unpleasant is basically another psyop