“Let me ask you, do Britons who can do otherwise opt to use NHS?”
Some do, just as some Americans who can afford insurance choose not to buy it.
“When I had a medical issue in England, I don’t recall ever being offered a choice.”
If you were unconcious you will automatically have been taken to an NHS A&E as the ambulance staff would have no way of telling whether you had insurance or wanted private care. If you were concious it’s up to you to say whether you have private insurance or would simply rather pay for private - they’ll transfer you immediately if you don’t want to use NHS facilities.
Just google ‘private hospitals UK’ and you’ll see there’s hardly a town without one.
No, I would think it's nearly always a matter of affordability when Americans decide whether to buy health insurance. I have a MSA, which means basically I am self-insured, because I am self-emplloyed.
Regardless, in the US, one's method of payment does not, at least directly, determine the level or standard of care the patient receives.