If you’re trying to measure inflation of necessities, then non-necessities should be excluded. If you’re trying to measure aggregate, broad-based inflation, you need to consider aggregate, broad-based baskets of goods/services.

Even with the necessity bucket, things change century to century which I think should not be considered luxury. Electric utility service and internet access I do not consider luxuries, but they were obviously not available in 1850 and 1950, respectively.