In Germany, Lufthansa and German railways have had a cooperation called "Rail & Fly" for many years now, and they even assign IATA "flight" numbers to some trains and (I believe) allow checking baggage through in some instances. But last time I used it, the ticketing conditions said that it was my responsibility to take an early-enough train and allow for three hours of buffer, or I'd risk having to pay for a lost connection out of pocket.
That's compared to connections of as little as 45 minutes when changing planes in the same terminal. Airlines are incentivized to make that connection if at all possible, since they have to pay a compensation for any delays of more than three hours in the EU, including delays for missed connections.
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.
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.
Which provide connection to only a handful of Austrian towns / cities. For everything else (esp. international trains), you need to change at the Hauptbahnhof.