A quick look doesn't show a clearcut weight difference. The claim is more for a 'rounder' wheel and a 'stiffer wheel'
First order approximation fuel economy depends on the weight of the vehicle, given the same engine. Suppose that your vehicle weighs 1 metric ton -- 1000 kg -- 2200 lbs.
Suppose that an alloy wheel was 5 kg lighter. That would be 20 kg (25 if you have a full size alloy spare) lighter.
20 kg is 1/50 of 1000, so 2% lighter vehicle.
So you get 2% better fuel economy.
So each $100 worth of wheel set cost requires the use of $5000 (2% of 5000 = $100) fuel to offset it's cost.
If a typical midsize car gets 30 mpg, and gas cost $3 per gallon, then your fuel cost is 10 cents per mile. $5000 worth of gas is 50,000 miles. If your car lasts 6 times as long -- 300,000 miles, then a 2% fuel savings would pay for an expenditure of $600 for a set of alloy wheels.
Given the costs I saw at Tiretown, this is a non starter. Prices were over that per wheel, let alone per set.
Note: A higher mileage car would take even longer to pay off. But even a 10 mpg muscle car would require 100,000 miles to get to this same point -- which still isn't enough.
So financially it's not a win. How about environmentally.
Steel is common. It's cheap. The processes that make it turn fossil fuel coal to make coke (essentially pure carbon) which in turn removes the oxygen from the ore to leave iron. Mix stuff back in to get steel.
Aluminum is expensive. Huge amount of embodied energy, but most of that energy is hydro-electric. This in turn means that bauxite ore is shipped by ocean bulk cargo ships to where the electricity is cheap.
Most magnesium now is extracted from sea water, also a high energy cost.
The big difference in price come from several factors:
A steel wheel is made by stamping out two halfs of the wheel, then welding them together.
An alloy wheel is cast as a single piece, I think, then in machined to spec. This makes for a rounder wheel. Complex support ribs can be moulded in that make it a stiffer wheel.
Snob appeal. They're shiny, and bright, and pretty, and fashionable, and they are a way to say, "look at me, I'm cool" This always commands a premium price.