A little EUSS landmine

You can have EUSS settled status without any proof of CSI. However, it appears that the Home Office has now started enforcing the "CSI" requirements again. SO if you obtained EUSS and at any point prior to that you should have had CSI and did not, you could be denied eventual citizenship.

I've read this several places now, but here is the most succinct one.
https://www.mcgillandco.co.uk/blog/settled-status-holders-still-need-to-show-exercise-of-treaty-rights-for-british-citizenship.html

You can have EUSS settled status without any proof of CSI. However, it appears that the Home Office has now started enforcing the "CSI" requirements again. SO if you obtained EUSS and at any point prior to that you should have had CSI and did not, you could be denied eventual citizenship.

That's why  I suggested you kept your CSI's for you and your daughter, but now you are returning to the US anyway.

According to the EU's 2004 Directive of Free Movement of Persons, the EU's PR is automatic for those EEA citizens who were a qualified person every day in another EEA country and if they were not, then their 5 years to PR clock started again. As you know, the EU's RC can become invalid. The Settled Status is very generous and is being given to those who have only resided in the UK for 5 years, even if they (their EEA citizen sponsor) was not being a qualified person for 5 years.

Nationality laws are different to UK immigration laws and has different requirements that must all be met for citizenship to be granted.
Having settled status and being free from immigration control for 1 year if not married to a British citizen, is only one part of being granted citizenship.

If an EEA citizen (EEA citizen sponsor) was not exercising treaty rights in the UK and did not have permission to be in the UK under UK immigration laws, then they were not in the UK lawfully (and the same for their dependants). Overstaying is a ciminal offence under Section 24 of the Immigration Act 1971.

An applicant must be of Good Character and for overstayng, that means not overstaying in their previous 10 year history.
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/770960/good-character-guidance.pdf

Some are reporting they have been granted citizenship even though they did not have a CSI.

The UK brought in illegally working beng a criminal offence under the Immigration Act 2016 and there will be non-EEA citizens who worked in the UK when their EEA citizen sponsor was not being a Qualified Person. I assume the same with using the NHS without paying too, if they used the NHS at a time when they/their EEA sponsor was not being an EU qualified person.

The EU can't force a country to give citizenship and there will be those with the EU's PR in another EEA country, that cannot have citizenship of that country.

Yeah, we kept our CSI, although it's pretty much useless in the Covid era. We do still have it, though.

It's a tad on the sleazy side to sponsor an advert campaign aimed at EU pretty much telling them that they did not have to have CSI and all was well, just apply for EUSS.  Everything would be fine if you get settled status. Right. Well, now they know where a good number of EU are in this country. It'll make it easier to do what they did to the Windrush people, I guess, and they can always pop up with the "we never said...." schtick.

One of the reasons we are leaving: non-citizens are at the total whim of the HO, who change interpretations of policy to suit the preferences of whatever political entity is currently in charge. Sometimes retroactively. Some of those non-native Brits who have gotten citizenship may be surprised someday when the HO decides they're no longer desirable and strips them of it. Not cool. And not out of the realm of possibility. I have lost what faith I had in the fairness of the legal/legislative system here.

Yeah, we kept our CSI, although it's pretty much useless in the Covid era. We do still have it, though.

The government have listed Covid-19 as one of the infections where treatment is free on the NHS, even for visitors and those who have no legal status, to protect those who reside in the UK.

It's a tad on the sleazy side to sponsor an advert campaign aimed at EU pretty much telling them that they did not have to have CSI and all was well, just apply for EUSS. 

Settled Status is all the EU's PR is, settlement.  The EU does not promise citizenship of that EEA country. The UK's Withdrawal Bill does not promise citizenship either.

Settled Status, like the UK's ILR, allows these holders to work in the UK,  claim benefits if they meet the HRT, use the NHS bill free if they are residing in the UK etc. They get what British citizens who reside in the UK can have

Anybody with settled status or ILR, can be granted citizenship IF they meet the Nationality laws.  All immigrants are treated the same when it comes to the Nationality laws, they all have to meet the requirements and pay the fee and there never has been an exception for those using EU rules.
e.g.
- An EEA citizen needed to present a DCPR to apply for British citizenship, as that proved they had been been an EU "qualified person" for 5 years continuously in the UK and held settlement; these had been lawfully in the UK. A DCPR wasn't issued if they had not followed EU laws, such as not having a CSI.
- Overstayers for months/years in the UK and who then used an EEA citizen to stay in the UK and eventually got the EU's PR (settlement) are refused British citizenship if they have been an overstayer in their previous 10 years. The same for those who marry a British citizen.

Some of those non-native Brits who have gotten citizenship may be surprised someday when the HO decides they're no longer desirable and strips them of it. Not cool. And not out of the realm of possibility. I have lost what faith I had in the fairness of the legal/legislative system here.

If they have used deception, in any application even if not used for citizenship, then thay can lose British citizenship and that is the same for all immigrants.
Those born British can lose their citizenship too if they are deemed to not be conducive to the public good and if they hold another citizenship, or if the Home Secretary thinks they have a claim to another citizenship.