My experience with US embassies (both the one in Brussels and Dublin) has never seen them refuse entry to a US citizen and tell them to re-schedule. They usually have separate entrances as well with different procedures.

Well this was in London. It's a large embassy obviously. They do have separate entrances--we went to the US Citizens one. We were blocked from even entering the security lobby at all--the outermost door to the street was locked and the guard who cracked it open gave us a postcard with the embassy contact information to make an appointment. I called them immediately and explained I was in front of their building and could I make an "appointment" for right then, but they said I had to use the website. Which told me there was a 10-day wait.

As I said, apparently this practice was instituted just last year.

From my (albeit limited) observations I thought they never turned away citizens but obviously I was wrong. Getting appointments with the US embassy can sometimes be a challenging ordeal. They do however make allowances for emergency appointments which can be very helpful at times.

Yeah, in general they help citizens pretty well, and help citizens a lot more in dangerous places. Although to get US citizen services in Baghdad was really complex; despite it being inside a fairly secure area (the "Green Zone"), I wasn't allowed to carry inside, had to make an appointment a week in advance, etc. I ended up just making friends with people at a nearby heliport who had badges to escort me in. It turns out most of the extra security was because they had slightly better quality food than the nearby military bases, and were trying to keep military people and contractors from eating all of it.

The Embassies in Bangkok, Abu Dhabi, Kuwait, etc. were all excellent, however.