Depends on where you are in the US. Arlington County, Virginia has no governmental subdivision and thus “Arlington, VA 222xx” is in the mailing address.
Your OP mentions the UK’s use of counties. That reminded me of Liberia. Liberia is officially divided into counties, not states or provinces. I just looked at the mailing address for the US embassy in Monrovia, which is in the county of Montserrado. The mailing address does not include the county. I find that odd.
As I mentioned, it’s now wrong to use counties in UK addresses. They were part of the official address until a few years ago, but the Royal Mail county boundaries had become very different from local authority boundaries, and so were very confusing for a lot of people.
Into this century, you had official addresses that used counties such as Middlesex or Banffshire that had not existed as local authorities for 40-50 years. Or you would have towns such as Bo’ness that had not been part of the West Lothian local authority since 1975 but still had it as their postal address. Or even more confusing, a town like West Calder would now be in the West Lothian local authority but its official address would be Midlothian, which continued to exist as a separate local authority.
And worst of all you had some places such as Ullapool, Cromartyshire, whose address was a county that had only ever been a widely dispersed joke that disappeared around 1890.
People ignored many of these official addresses for years and the post still got through, thanks to the postcode. But address databases still list them, to people’s confusion and annoyance.
The bolded part is not correct for Germany. If you want to send mail to Neustadt an der Weinstraße, you address it to street address, 67433 Neustadt, and if the mail is for Neustadt in Sachsen, 01841 Neustadt. The different towns are unambiguously differentiated by their 5 digit postal code. State or other communal divisions are never needed for a German post address, though many people would write “Neustadt an der Weinstraße” or “Neustadt in Sachsen” to avoid any ambiguity in these cases, but that’s optional.
Sorry, I should have made it clear that I was talking about referring to those places in general and not specifically about mailing addresses. For example, I compiled a Wiki-list of certain places in other countries based on other references. Occasionally, some reference book would have a town in some European country where it turned out there was more than one with that name. The reference didn’t distinguish which one, perhaps because the author didn’t realize there was more than one. At any rate, I ended up having to say [disambiguation needed] for those entries. Not that I ever expect to get any.