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.
Luxuries change century to century and within decades but those hardly matter for inflation since those are by definition not necessities.