Most of the exemptions are for e.g taxes on fuel, or land taxes for airports etc. Taxing flights the same way e.g cars are taxed would make trains more competitive, but wouldn't really lower the price for trains. In many places train infrastructure is also heavily subsidised.
The sad reality is that air travel has much lower cost for fixed infrastructure (≈ airports) compared to trains, per passenger km. If we build an airport, an airline can more or less just fly wherever from that airport. If someone wants to fly 2 hours west to a large city, and others would like to fly 2 hours south, they can just do that without really impacting the other (except for taking up slot times).
With trains every single km of track you lay can only be used going in that direction (duh), and needs to be maintained year around. You have expensive tunnels, bridges and "advanced" control systems and infra all along the track. To extend the rail network to another city is an enormous up-front const, and only "unlocks" one new city (or direction). A (large) airport can be used to go both 45 minutes away on domestic flight or half across the globe.
Tracks form a network that can be used to reach more than just the directly connected cities.
Similarly, airports require a high up front capital cost and form a network that allows you to reach further than the infrastructure at the starting point allows.
On rail having high maintenance cost for the infrastructure: every flight requires expensive and fragile planes + lots of fuel, so the marginal cost of each trip is high.
So it's a little more complicated to compare the costs than you suggest.
The sad reality is that air travel has much lower cost for fixed infrastructure (≈ airports) compared to trains, per passenger km. If we build an airport, an airline can more or less just fly wherever from that airport. If someone wants to fly 2 hours west to a large city, and others would like to fly 2 hours south, they can just do that without really impacting the other (except for taking up slot times).
With trains every single km of track you lay can only be used going in that direction (duh), and needs to be maintained year around. You have expensive tunnels, bridges and "advanced" control systems and infra all along the track. To extend the rail network to another city is an enormous up-front const, and only "unlocks" one new city (or direction). A (large) airport can be used to go both 45 minutes away on domestic flight or half across the globe.