Sitting implies to other people that you're lazy and lack a work ethic, because anyone with a drive wouldn't be a cashier. In reality people just need a couple moments relief from the back and foot pain. Not even slightly taking some weight off by leaning against a stool is permitted.
This type of perspective can easily start to infiltrate technology. Someone already made a comment about how they thought this would be about managers forcing people to use standing desks. Do you want to be passed over for a raise by management because you sat down at work while coding for most of the day, compared to co-workers using a standing desk?
(I don't know if this is normal for Aldi, but I mention the name because of relative uniqueness of Aldi in the U.S. compared to other grocery stores).
Aldi is a German company. Every grocery store I've been to in Germany has seats for the cashiers. Also, the cashiers wear name tags that read Mr. or Ms. Blah.
I suspect parent is correct about this being mostly an American cultural thing.
I should also add that it's not 100% that everyone has this perspective, and it could vary by region in the US. Sometimes it's employers who think that customers might perceive this. It might even just be the case of a vocal minority of people who think everyone else doesn't work as hard as them.
I worked in a grocery store (in the US) back in the day. People complained about the smallest stuff -- that I wasn't as conversational as they wanted, or that I wouldn't process their coupons in the order that they expected, or even in one case that I wouldn't help them steal from the store.
Maybe 1 in 10 complaints I received was even remotely close to something a sane human would be even mildly inconvienanced by (and even for those I can't imagine ever caring enough to spend my free time complaining to a grocery store manager). It wasn't just me or just that store; management had an entire formal process passed down from the corporate office for figuring out which complaints should contribute to evaluations and which were spurious. I never had less than 10 complaints per quarter and only two of those were mentioned in my evaluations over a several year period. Other cashiers had similar numbers. Interestingly, friends who worked at non-grocery-stores encountered these sorts of things far less often.
I'll never understand the psychological reasons for why people behave like this. It's probably the same reason people troll. But I do wonder whether it's a US-specific phenomenon wrt grocery stores specifically.
Since it's well known that cashiers (especially at grocery stores, but in most countries this is a general thing) are not that well paid while the work is all about speed and efficency (aside all those unpaid overtimes, at least in German discounters), it tells much about prevalent work ethics.
It should be
"Why on earth should those people stand while doing this monotonous work everybody needs to get done?"
instead of
"Why are those lazy people are allowed to sit while taking my hard earned money?"
But I doesn't think that those customer happiness advocates do care much about those trivial considerations.
I do agree, completely, it is torturous. I've done it many times, and only at a school was I ever allowed to sit without getting written up. Weirdly, the employees comfort was rarely an issue.