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First, it doesn't save fuel.
"Auto" mode sends some power to the rear wheels a little, coming from a full stop, even if no slippage is detected, so it gives that nice "RWD push" feel.
2WD mode seems to "feel" a bit lighter on the engine, but it tends to spin the front wheels on hard take offs, and give that oversteer tendency when turning while accelerating.
So, is there any practical reason to use the car's FWD only mode?
Typically part time 4WD is not the same as AWD. Part time 4WD will actually lock the front and rear axles together, not providing a differential between them to handle the speed differences between front and rear wheels while turning. As such driving a part time 4WD in 4WD on pavement is a great way to break things. Auto is intended to give you 4WD when it's safe to do so without destroying your drive train as you take turns. It's best with a part time 4WD vehicle to use 4WD when the need arises, and use 2WD most of the time. AWD (or full-time 4WD) vehicles are always sending power (with varying distribution depending on manufacturer and conditions) to all four wheels.
It seems awfully strange that a part time 4WD would be FWD then in 2WD mode, as most part time 4WD vehicles are trucks. Are you sure it's FWD in 2WD mode? Also, if you're spinning your tires from a stop when it's dry, you should probably learn to adjust your driving habits or get better tires.
Now, on to your car. You really should've told us make and model, as that would've been useful information for an answer tailored to your vehicle. Luckily I was able to find this on the Nissan website without much effort:
The ALL MODE 4X4-i* switch gives you a choice of three different drive modes for the optimum distribution of power. 2WD mode shifts power to the front wheels for fuel-efficient city driving. In AUTO mode, the X-TRAIL analyzes the terrain as you drive and precisely distributes the right amount of torque to each wheel for the best handling on any surface. If you need extra grip, LOCK mode fixes torque at the optimum front-rear ratio for confident 4x4 handling in snow, sand and rough terrain.
This sounds like it has the capability of both a locking and differential behavior between front and rear, so it's certainly designed to operate either way. Provided your tires match, it might be beneficial not only for traction, but also more even tire wear to stick with the auto 4x4-i mode in normal driving. When the standard drive wheels are rear, there are several reasons to use 2WD only. When the standard drive wheels are front I cannot come up with any reason to run 2WD other than when running on a donut or with mismatched tires between the front and rear axles. Note the claim here is that 2WD is for efficiency in stop-and-go driving, which disagrees with your assessment that there is no difference in fuel economy.
When comparing FWD to RWD, they each have their separate advantages: RWD is better off the line (as you've testified to), and FWD is better while maneuvering in and out of places with horrible traction (like parking in or leaving a snowdrift). But if AWD is an option, it does provide the best traction, albeit at the cost of some fuel economy and added wear to the diff.
