> they stock the store with a rotating selection of random crap that fell off the boat, baiting the impulse for an aspirational or just-in-case buy

I believe this is the key to their fanatical customer base. The random crap aisle means that when you go into the store there's a chance of an awesome deal on some random thing. This provides strong intermittent reinforcement which directly triggers the brain's reward mechanism, no different to loot drops in an MMO or payouts from a poker machine. People literally get addicted to Aldi's random-stuff aisle.

We've actually taken to referring to Aldi as "visiting the casino". :P