I don't know how they compute the COLA on SS but retirees should have a different basket of goods and services than working people.
A retired person usually isn't buying a first home, paying daycare, buying new cars or going to college. They feel the effect of food prices and medical care prices more and gas prices less. So the cost of living in a paid off home, heat, lights, food, car repairs and insurance should be weighted more heavily than the price of houses and daycare.
My mom has been retired 20 years and lived in a paid off home for 30 years. Her cost of living is about $500 a month for utilities and property taxes and $800 a month for food, gambling, gifts, decorating, gas, car repairs. Until a year or so ago she was budgeting $400 for spending and gambling but doubled it so she could gamble more. Now she has pretty much stopped gambling and still is using up her $800.
She is selling her house now so will pay rent but have the income from carrying the contract on the house of 1,250 a month. She isn't involved in selling the house or how much rent she will pay but my brother is taking care of it and told me the contract on the house but not what her rent will be. She will be living in his house so he will provide all the food.
For a poor elderly person food and medical cost is much more important than the price of houses.