The NHS isn't perfect, but one of the things it does well because of it's structure is minimise costs holistically. It's cheaper to treat conditions early, so usually implements appropriate screening to catch things. If they don't do regular checkups like this it's because they're of minimal value.
In the US case specifically, I always wonder how much of the benefit is just “here’s a free appointment with a doctor once a year”.
The idea behind physicals is they're considered preventative care... catching problems early, often before there's any overt symptoms. For example, checking your cholesterol and A1c levels before they progress to heart failure or diabetes.
Once you're showing symptoms, you've left the realm of preventative care and it's now diagnostic/treatment for a established issue.
(ACA only provides 100% free coverage for visits that are 100% within the "preventative care" box.)
I think I'd prefer the UK system where if you worry something is wrong you can see a doctor free of charge.
I think that there's a working assumption amongst US folk that because the NHS is is publicly funded, it must be terrible.
US healthcare plans offer an annual physical exam every year at all ages. Looking at the UK NHS website, it seems to be only offered there after age 40, and limited to once every 5 years? Am I reading that right?
I thought it was relatively uncontroversial that the major problem with US healthcare is not quality but cost. And the UK NHS is widely regarded as one of the lower quality implementations of single payer in any modern social democracy [0].
[0] https://www.usnews.com/news/best-countries/rankings/health (#23, but Canada is actually worse!)