Speaking from experience, the 10-20 euro fares are not always available on flights. But then again, cheap fares are not always available on the trains either, especially at the times most people want to travel (Friday or Sunday evenings, etc). Also flying takes longer because the airports are not as central as the train stations, and you need to go through more luggage checks, board with more time to spare etc.

I think competition has helped drive down flight prices, and since they opened the Madrid-Barcelona high speed line to competition prices have dropped a lot for the train as well. If you compare Madrid-Barcelona to Madrid-Sevilla for example, the price difference is really high and much more than the distance would imply.

Train systems are basically governement monopolies and thus run super inefficiently.

Public transports should be public.

Government monopolies don't have to run super inefficiently, and many times they don't. Also look at how many private companies fail (especially startups): private companies are not a safer bet.

Not in Europe they're not; thanks to Open Access you have your choice of three different companies to take a train between Madrid and Barcelona, only one of which is the state carrier.

Oh please, Tell me how much public funding those other two companies receive. I dont count a company that cannot survive without government funding as a private company.

That pricing feels backwards.

Airlines don’t pay their externalities

It may feel backwards, but it is real.

While we never saw the 20 Euro airplane fares, for some reason the train fares were almost always more 20-50 Euros more expensive than the plane fares given the same lead times.

It was quite irritating.