The cost of food is obviously going to vary depending on location, but it's pretty well proven that healthier, more nutritional foods tend to be more expensive than the less healthy, mass manufactured alternative. Ground beef, rice, and beans alone do NOT make for a healthy and balanced diet, even if they are cheap. Next time you're shopping, compare the price and ingredients of fresh vegetables vs canned or frozen. Compare the breads, dairy products, grains and cereals, snacks, condiments, etc. You'll almost certainly find that the more affordable options are loaded with far more preservatives, additives and various sugars.
While a cooking class may help a person make better choices with their diet, it will not change the fact that a large portion of the population literally can't afford to eat healthier.
It's true that poor people pay less in taxes, but the taxes will always have a much greater impact on their lives compared to someone with higher income and therefore more available money. If someone makes $1000/month and pays 20% tax, they only have $800 left. Compared to someone that makes $10000/month and pays 30% tax, they still have $7000 left over. Assuming they both live in the same area and pay the same bills, which one is affected by a tax increase more? Which one is going to be able to afford the more expensive, but healthier foods?