The economics are quite involved, and can be easily skewed depending on what externalized costs you choose to include in your analysis.
Superficially, flying has relatively lower infrastructure costs because it only needs the two endpoints (no road, no track, no bridges, no tunnels -- all expensive items). That impacts both the initial capital cost, and the ongoing investment in maintenance.
Similarly, planes are fast: above a fairly short distance, it's much quicker to fly (by jet plane) than to travel by train or road vehicle.
But airports are difficult to access, being unwelcome in the middle of cities, and so there's a need to get to the airport as part of your journey. That part of the trip likely requires road or rail transport, and it's the most capital-intensive bits of the road/rail (ie. through urban areas).
The fuel cost of planes is also higher per passenger-distance. And beyond just simply purchasing the fuel, it's much easier (for instance) to electrify a train or car than a passenger plane. So how you account for the carbon cost will make a big difference to your result.
For the last 20 years or so, short-trip flights have been superficially cheap. The most obvious missing cost is the impact of using fossil fuel (and potentially that's even worse at high altitude), but there are other factors like the (ab)use of precarious labour, government subsidies for both fuel and facilities, noise impact, etc.
Whether it's ultimately sustainable or not all depends on what costs you choose to factor in.