>It doesn't work that bad with cross-border metro areas in the EU. Or at least the ones I know.

It doesn't work that bad in the US either, but there's tons of room for improvement. But, just like the EU, in the US neighboring states are usually at or near economic parity; this is not the case for US/Mexico. Imagine having a city in the EU that's half in Germany and half in Greece (suppose there's a freak seismic event that moves the two countries together).

>I live in one, it's perfectly good. Maybe I wish the metro could have a few stations on the Belgian side of the border, but the buses do cross it so it's still fine.

Well obviously it's not fine, and could be a lot better. Why settle for crappy bus service when you can have a subway system that doesn't stop on one side of an artificial and nonsensical border? If your entire metro area was within one country, you wouldn't have this problem; if it made economic sense to the city to put in those metro stations, they'd just do it, and wouldn't have to mess around with a bunch of international (though at least intra-EU) political problems to get it done. It's not easy to build infrastructure that crosses political boundaries, and especially national boundaries; look at the Chunnel. How long did it take them to finally agree to do that?

>By the way, it not only spans across France and Belgium, but also across Flanders and Wallonia on the Belgian side

That's probably not a big deal because it's in the same country, and I'm guessing different regions within Belgium don't have quite the autonomy and political bickering that separate US States do. But spanning France and Belgium isn't as easy. Now, imagine that your city spans France and Spain; don't you think there'd be more problems? How about France and Italy? Italy and Croatia? France and Switzerland (which isn't EU)?

>But there is one common metropolis authority that the transit agencies have to answer to and that coordinates what happens in the metropolis, it's like the inverse of what you're describing in the US apparently.

We have that too, but it's frequently a mess. In metro areas that are within a single state, there's usually a single metro transit authority that runs the buses (not that many cities have subways here). In DC, there's a single agency that runs the subways, which run between Virginia, Maryland, and DC, and that agency is an utterly corrupt mess with horrible service and fatal train accidents. In New York, the MTA runs the NY subways and buses and the LIRR (Long Island Railroad), but then NJ Transit runs the trains and buses on the New Jersey side, which also stop in Manhattan on the NY side, so there isn't a single authority there, nor a single transit system (so to travel between Jersey City and Brooklyn you'd have to take a PATH train or a bus to Manhattan, then get off and go to a separate station possibly, get on a subway with a separate ticket, and go the rest of the way; the entire trip would take quite a while because there's nothing resembling a direct route. It's much worse if you're going to the Bronx or Queens or Staten Island.). When there isn't a single government or single transit authority, there's no consistency and no single overall plan of how to implement an efficient system. And when there is a single authority (like in DC) but no single government, you end up with massive corruption and mismanagement because they don't answer to a single governmental authority.