Interesting question. I'd say the end-to-end traffic on the Meteor and the Star isn't enough to justify it. Nonstop trains are rarely the best use of trains; an extra stop can cost maybe a couple of minutes on schedule (at most) while bringing in hundreds of passengers daily.
In the 'old days', nonstop trains generally only existed on routes which already had lots of local, limited, and express trains -- and which had a particular character with a lot of end-to-end traffic. For instance, the "Twentieth Century Limited" ran nonstop from the Chicago metro area (which had 1 downtown, 1 suburban stop) all the way to the NY metro area (which had the same), but it was overlaying a whole lot of trains which stopped more frequently.
What would be the equivalent today? In the US, probably the NEC. The Acela is already providing the express role. But there's not enough traffic from Boston to south-of-Philly to justify a non-stop starting north of New York. And New York to Philly is stronger than New York to Washington, making it hard to justify a non-stop from NY to Washington. While NY to Philly is too short to bother with an exclusive nonstop train...
I don't think a proper non-stop would be successful in any corridor at the moment. However, as train service extending south of the NEC increases, there's probably a market for some more "limiteds", making only major stops. I could imagine a Norfolk Limited, stopping only at Norfolk, Richmond, DC, Baltimore, Philadelphia, and NY.
The Auto Train is only non-stop due to how time-consuming and annoying it is to load/unload cars at multiple locations.
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A more interesting question would be whether additional Auto Train services would be successful. They've tried Chicago to Florida, but it couldn't be made fast enough to be popular. Chicago to Arizona was considered in a recent PIP, but rejected as having worse cost recovery than the existing Auto Train and not worth it.
I think there is one really natural extension: get a northern terminal of the Auto Train further northeast. It is known that lots of the customers are coming from the NY area. You'd probably want to retain the Lorton terminal, but you really want a terminal up in New Jersey or even Connecticut. This has been prevented by a lack of rail routes with sufficient clearance. It should soon be possible to get autoracks through DC due to CSX's clearance work on the Virginia Avenue tunnel. I believe the next major obstacle is Baltimore. If the multibillion dollar new tunnels (tunnels for freight and tunnels for passengers) which are currently planned are built in Baltimore, it would likely become possible to get an Auto Train all the way to the Jersey suburbs of New York, and I'm sure it would be possible to build a terminal there. (New York is the next major obstacle.)