Why use multiple materials on chainrings? Why is it that on a typical mid-level road triple crankset, the outer rings (larger rings) will be aluminum, while the inner ring (small ring) is chro-mo?

It seems to me that if aluminium was good enough for one, it'd be good enough for all.

Does it have to do with the amount of force applied to each ring? Perhaps the smallest ring is likely to be used in climbing situations, when the cyclist is standing, so the most force is being applied to the crank at that point (and thus you need a stronger ring)?
This is actually a matter of the force multiplication that each chainring provides, and the size/mass of each chainring.

Force difference

Let's propose, only for a moment that you had a chainring as big that the radius of it is almost the same as the crank length. If the rider stood to pedal while using that chainring (and using simple platform pedals). The max theoretical force on the chain will be equal the the rider's weight. (Assuming he/she is not pulling on the handlebar).

Now, let's get rid of that impractical and ridiculously large chainring, and install a more realistic one, one that has a radius of approximately half the length of the crank. Now when the rider repeats the previous experiment, now, the maximum theoretical force applied the the rider's weight*2.

If you repeat the whole experiment, but this time with a chainring having a radius of 1/4 of the crank length, the maximum force in the chain would be 4 times rider's weight.

That is, In a simple mechanism like a crankset, the output force can be calculated as:

OF = IF * (Ir / Or).

Where IF = Input force, Ir = input radius, Or = Output radius. And radius is the distance from the axle to the point where the force is exerted.

As you can imagine, most tripe chainring crankset have a large chainring that has a radius roughly half crank length. An the smaller chainring is half as big. Effectively, the typical triple crankset doubles the output force in the small chainring relative to the largest.

Weight matters

However, this is only part of the topic. The bigger the chainring, the heavier it is. And it is also a rotating part of the bike, so, some may argue that it's rotational inertia would matter. As you can guess, CroMo chainring are heavier than Al.

Durability

That still doesn't fully explain the decision, but here it goes: aluminum typically has less resistance against friction wear than steel. For example, if you had to file down a bump in an aluminium piece, you would do it with low effort, compared to the similar job on even mild steel. Added to this is the fact that a new chain in a new chainring engages several teeth with full roller-tooth contact, effectively spreading the load among each contact point. The small chainring can provide less contact points to spread the load, with means that each tooth is subjected to a bigger fraction of the total force applied by the rider and multiplied by the crank. That means that a tooth in the small chainring bears a much greater load than a tooth in the big chainring.

Usage ratio

Into this we can add the rather subjective argument that most riders would spend more time in the middle chainring, perhaps in the small one or jumping a lot between them, while the large one is used more sporadically, usually in fast descents where the rider won't use his/her full strength and not for long.

Conclusion

All of these arguments make the chosen materials good compromise between weight, durability and maybe, cost.

Aluminum small and middle chainrings would wear out too fast, and would be prone to bending from incorrect shifting technique. A big chainring made of steel would be heavier and the difference would be easily perceptible while holding the crankset in hand, so the crankset with the aluminum big chainring would make the best buy among the two.

The weight difference between small chainrings made of these materials would be less perceptible, and the buyer may not be so appealed to pay the price difference for such a small weight loss(gain?).

Also, aluminium small chainrings may be better suited for professional riders, whose may ideally be properly sponsored, so spending a chainring per race is not a big deal. Also, he/she may (ideally) have an optimized shifting technique (i.e. the rider has identified his/her shifting technique faults and has corrected them).