No it works because you use fat for energy rather than carbs/glucose, it's that simple. I don't drink milk, I only have dry aged cheeses and the best meat/fish/protein. No bacon or deli meat crap.
Yeah food is more expensive on keto but that's not a reason to avoid it. You can go to Aldi and pick up some well-priced grass-fed meat cheaper than Tesco or Sainsbury's or Waitrose (if you're a knob).
Chicken thighs taste better to me, but I also eat Chicken breast. I don't eat pork which cuts out most garbage protein. My breakfast (2pm) is usually steak and eggs with some vegetables. Or Haloumi, mushroom, chicken tomatoes, cheese all the cheese I want. Nuts (Macadamia, Brazil, Almond) seeds (chia, hemp, flax, pumpkin). Lots of eggs, avocado, avocado oil, macadamia and coconut oil. You can eat lean meat, chicken breast etc and get your fat from the oils.
It works for me, it's not for everyone. I got most of my info from
https://www.youtube.com/@ThomasDeLauerOfficial as he is muscular and does keto.
I don't even want carbs or sugar.