What if they ran their .asl file as a spot color, could it print on the web press then?
Also. Running a job on a web press has the advantage of inline finishing. This decreases the number of hand touches, which means less mistakes. There are different QA levels set on the amount of automation. Print quality is the same, product... depends on the day.
The simple fact remains that USPC won't do a web-press run for less than 10,000 decks. I'm nearly certain that at that point, they'd be insisting on increases in units of 10,000 decks as well, due to the size of a paper roll. A single paper roll, start to finish, makes about 11,000 decks providing them their 10% margin of error on the plus side. Once the web press starts rolling, nothing short of a disaster on the floor will stop that run before the roll runs out.
In theory, when ordering 10,000, they're making 11,000 then removing anything damaged, misprinted, whatever, as well as uncut sheets, which I imagine are a challenge (though not an impossible one) on a continuous press like the web press. This means they can remove as much as 2,000 decks from the run for quality control or whatever other reasons and still meet the contract requirements.
Companies like Ellusionist, The Blue Crown, Theory11, David Blaine, Dan and Dave, etc. tend to deal with USPC in these numbers for their staple decks or limited-run decks where the quantity isn't public knowledge.
As far as inline finishing, what would make you think that the process isn't done on the line for the sheet-fed press? They're using a modern Heidelberg press - damn thing can practically tie little bows around the cards if you wanted it...
There is exactly one advantage to be had with the web press - speed. But the increase in speed isn't that much faster from the perspective of the designer/producer - start a print run on either press at the beginning of the day, it'll be done long before the day is over. It only makes a difference to USPC, in terms of how many runs they can squeeze into a day.