I'm EU who never lived in my home EU country. The Daughter is a USC with me as a dependent family member (all legal and above-board). I would love to work but have not found a job. She is in higher education for the next several years.
Because I am self-sufficient (supporting us both), we are both required to have "comprehensive sickness insurance" - basically the top-of-the-line health insurance. It isn't cheap. I pay taxes on my self-sufficient income to the UK, as well as a stiff council tax and the usual VAT, just like everyone else. Yes, my ex-employer is covering the cost of my CSI as part of my pension package. And I have to pay UK taxes on that as a benefit, even though it's insurance that has a wonking big deductible and only covers 80% of "usual and customary" charges.
You are under EU rules so that your adult US citizen daughter can be in the UK. You and your daughter must have CSIs as the EU's 2004 Directive says that "ecomically inacitve" EEA citizens must have a CSI for themselves and all their "Family Members" to be a "qualifed person" to have a "right to reside" in that EEA country. If you didn't have them, then your daughter would be an illegal overstayer in the UK. Unlike UK "visas", the EU's RCs can just become invalid as the end date on them means nothing.
The EU says you don't need to pay working taxes to that EEA country, to be what they call a "worker qualified person" and then be allowed to have bill free use of the NHS for themselves and all their "Family Members".
The present UK government (May's government) allows those who are "economicaly inactive" to have bill free use of the NHS as long as they have a CSI to be a "qualified person" in the UK. Under present rules, you don't claim on your CSI when you use the NHS.
It's why the EU is saying that after a Brexit, regardless of what is in a Withdrawal Bill, the UK can bill these for their use of the NHS as that is what their Directive says; even if the rules aren't tightened again after Brexit on who can use the NHS bill free.
I WISH there was an option to just pay the fee to the NHS for cover and not have to carry the CSI - we'd come out ahead.
EU rules and UK rules are not interchanageable. You are using EU rules and the EU says you need to have CSIs.
Some people tired to use a UK EHIC as their CSI
They lost in court.