From my experiences in Europe, it varies by Country.
In Sweden, most of the POs have been closed - You buy stamps at convenience stores, mail packages at service desks in Supermarkets - Packages are delivered to the closest supermarket and you get a text message or postcard in your mailbox where to pick up the package.
In Austria the POs are thriving and you can buy cards, bank, get phone service, buy a cellphone and get lots of other services at the PO.
From what I understand part of the problem in the US is that postal unions do not want the work outsourced to a grocery store, Staples, etc.
When I was growing up in Scranton, PA, in every neighborhood had a pharmacy that had a PO counter. When I moved to Amherst, MA in the early 80s the pharmacy in downtown had a PO counter where you could mail a package or buy stamps anytime the pharmacy was open. Alas, the pharmacy has been replaced by a CVS where you can just buy books of stamps.
In the 70s in Providence, RI, the main PO had driveup window that gave some services 24 hour a day. I'm not sure that trend continues to this day.
Of course, now 95% of my work-oriented mailing is done by email, so a late open PO is not always that needed.