It might be that a lot of the cost doesn't show up in the data because it comes out of your paycheck before it's "yours," in the form of your employer's contribution to health insurance premiums. (Anecdotally this is true for me - "my" portion of premiums would not be in the top three, but the total premiums are #2 after housing (for a while when I had roommates they were #1, which is ridiculous).)
Correct. You can argue this is money that you’d otherwise get if it wasn’t going to healthcare, and that’s a fair point. But then you have to count that in the top line income.
(BLS gets this data from surveys: https://www.bls.gov/opub/hom/cex/home.htm )