AIUI, you lose energy because the power/torque has to go through an extra differential, transfer case, etc, before reaching the rear wheels.
Going from the engine through the transmission to the front wheels is already a 'fixed cost', but the extra mechanics (and their friction loses) to the rear wheels an 'OpEx' that you don't necessarily have to pay if you don't need to.
True for a FWD v RWD car decisions, but in an AWD are not the rear differential and driveshaft still turning whenever the rear wheels are turning? Even the clutch packs should still be rotating even if disengaged. The fact that there is no power through them doesn't mean they aren't generating losses.
It sounds like the savings are more in construction costs than fuel savings.
If your back wheels are rotating at the same speed as the front wheels while you turn, then you'll induce wheelspin on the rear and potentially lose control, or damage your tyres, drivetrain, or engine.
Full-time 4WD and AWD cars have three diffs, one on each axle, and one between the two.
Others have mentioned the RAV4 which actually has two separate drivetrains, which is a different implementation all together.
Most RWD and 4wd vehicles are longitudally mounted, allowing for easier packaging of power to the rear of the car.
The transverse packaging works much better in FWD configuration as
1. Packaging; the relation of the "AWD" (mostly FWD) transmission and a tranvserve engine is naturally a smaller form factor than other combos. Plus, the lack of traditional diff/transfer case is tons of weight savings.
2. Average driving; "FWD mode" in AWD vehicle is functionally equivilent to a FWD vehicle. This is ideal for most driving, IE; snow, fuel economy, understeer etc.
The clearer distinction is that a 4WD has a second gearbox (aka a transfer case) that either manually or automatically engages the front wheels, the Jeep Wrangler /TJ being the architype.