sure, that's why I mentioned "<600km", which is a distance covering many connections in Europe. E.g. Paris-Milan, Amsterdam-Berlin, Budapest-Vienna, London-Brussels, Geneve-Genoa etc

These would be

* many hours by car * <3 hours by fast train * <1 hour in flight by plane

The flight time is offset by security controls and getting to/from the airport, so a fast train is a good alternative (not perfect, just good).

There is also always the comfort factor. Increasing travel time by 25% or even more can be a non issue if I have high speed internet and proper food and drink service available.

It's an investment though. Every part of France that's next to the high-speed train really blossomed.

In France pretty much anywhere near a high-speed train station becomes within convenient reach of Paris and so attracts a boom in second homes and hybrid/remote workers.

Different optimal solutions for different scenarios.

Not really. Flying is fast, but when you measure door to door, in distances of under 1000k, a high speed rail network would not be slower.

Hence "as distance grows"...

But a 1000km radius around any major center in Europe covers a lot of potential destinations. I assume that a lot of people, especially in the US underestimate the density of Europe.

1000km is a stretch to set the threshold at which trains win on time. It is also costly, not least when you hit a mountain range... at some point you need to balance billions of euros vs saving an hour (or even less).

Is that always true? In France HSR stations are often like airports, way out of town and you have to get a taxi in/out of wherever you're going. And the rail network seems more exposed to mechanical breakdown in general. I don't have hard data but it feels to me like trains fail or get cancelled much more often than flights do, and when a flight does get cancelled it's usually due to some major failure that'd take out trains too (e.g. power failure).