You're free to come up with your own index with your own basket. The BLS publishes inflation indices at a very granular level, so you don't even need to reverse engineer their data. For maximum shock factor, may I suggest a basket overweighted towards medical care, college tuition, and healthcare[1]?
I wondered why you had medical care and healthcare, they seemed redundant, but good on BLS for separating hospital costs and medical costs. That truly is granular.
Do you have a better one you use instead to gauge inflation?
Even if they don't, that's not a valid argument. A metric can be misleading even in the absence of better ones. The parent comment does not deserve the downvotes.