Power and fuel economy are not the only two variables. Emissions are the biggest thing that comes to mind: your new high-performance remap might put your car outside of the emissions limits for your market.

Some aggressive remaps can also adversely affect how the car drives in normal use. Think rough idle, or jerky acceleration. The vast majority of drivers do not want that.

Factory tuning is done the way it is for fuel compatibility, engine and component longevity, and a wide range of consistent performance at any reasonable altitude.

Changing the timing of the ignition, altered valve timing, and changing to a higher octane fuel can give you more power and better crusing economy at the cost of longevity, not being able to use a lower octane fuel, and possible issues if you drive at an altitude far different than the one it was tuned at.

Engines are tuned for emissions, not power.

By sacrificing emissions.
You can get more power per stroke if you don't care about emissions, and that can get you a better fuel economy, but you may fail your local e-check if it's tuned.

Volkswagen got in trouble for designing their cars to change the engine tuning when it detected it was connected to a testing rig.

It can't do both at the same time.

By remapping I assume you mean changing the ECU (engine control unit) programming.

Depending on what all it controls, usually fuel injectors and ignition, and what it reads, air pressure, rpm, oxygen, throttle input, the mapping adjusts timing of ignition, and how much fuel is injected based on how fast the engine is spinning, and where the throttle is set.

Most cars from the factory have a very simple mapping based around what most drivers do.

A fancy prototype CRX I had back in the 90s had very custom mapping that meant when I drove mellow, it got about 45 mpg, but had very slow acceleration. If I pushed the throttle past a certian point, it spun up like a bat out of hell, but the fuel economy would plummet.

What you can do with custom mapping is change the way the engine behaves under various conditions and based on the inputs. There is no magic get more out of the engine. Want more power? Eat more fuel and lose economy, and likely not burn off all the fuel so more dirty exhaust. Want more range? Limit power and lose acceleration.

If something promises to increase power and economy at the same time I assume it's bullshit.

With that said you can increase one or the other with remapping depending on your focus.

This is something I've played a little bit with in Forza Horizon, and after reading these comments, I think it would be cool if they added emissions as a metric in their engine simulations. Of course I'm sure that would also lead to folks rolling coal in-game.

All depends on where you're starting from. If I can map an engine to be worse on both, then a mapping exists that is better on both.

Think of it this way:
if you modify and tune an engine to make more power the energy conversion is more efficient. A more energy efficient engine will be able to perform more work with less fuel.

So while it won't have better economy on a power run, it could have better economy while cruising.