I mostly fly from Vienna, Prague and Budapest and none of them have fast rail connection.
I think this is a hard problem, since the rail lines naturally converge in the city, at the airport you'll get one rail line at best and quite likely need to change in the city again.
Vienna airport is definitely serviced by Railjet trains (Austrian railways' high-speed product) stopping directly at the airport railway station. The same is true for Frankfurt am Main (one of the largest airports in Europe, serviced by ICE trains from all over Germany).
The point here is to replace a shuttle flight from a hub to a satellite airport of an airline/alliance, and for that to make sense, there needs to be both high-speed rail infrastructure from a given city to such a hub airport, and a train station at the hub airport.
> Vienna airport is definitely serviced by Railjet trains (Austrian railways' high-speed product) stopping directly at the airport railway station.
Which provide connection to only a handful of Austrian towns / cities. For everything else (esp. international trains), you need to change at the Hauptbahnhof.
I think this is a hard problem, since the rail lines naturally converge in the city, at the airport you'll get one rail line at best and quite likely need to change in the city again.