> Once you are no longer combusting fuel, all of that compression is simply wasted energy.
Not true. Instead of burning fuel, you can use electricity (something like an arc welder) to generate heat. And the efficiency with which that heat is turned into mechanical power will be dependent on the compression ratio, regardless of whether the thermal energy is coming from electricity or burning fuel.
Thermal energy in chemical fuel and the potential energy in a battery or a raised weight have the same units, but there's actually a difference. You can turn energy in a battery or a raised weight into mechanical energy with 100% efficiency - not achieved in practice, but there's no theoretical limit.
When you turn thermal energy into mechanical energy (via Otto cycle in a car or Brayton cycle in a jet), the peak efficiency you can achieve has a theoretical limit based on how much you can compress the working fluid (air) before injecting thermal energy (burning fuel or an electric arc).
So if you've got electic energy that you can turn into mechanical energy in a fan with 100% efficiency, why would you take the thermodynamic losses of "burning" that electricity? Because we don't know how to go supersonic speeds with a fan or propeller - the only way we know how, for now, is with a jet running on the brayton cycle. And all the advances we've made in high compression fuel-burning jets would apply to electric jets just as well.
If you're okay limiting your top speed to ~Mach 0.7, then you're correct spinning a large propeller using electricity is absolutely a better way to go, and you can make that propeller a lot bigger if you're able to tilt it.
Karem Aircraft has done extremely interesting work on figuring out how to tilt rotors, and much of their research would apply to electric motors as well: http://karemaircraft.com/