It really doesn't sound like a good example of the Doorman's Fallacy, which is about automation failing to provide the nonobvious benefits of a human doing the job.

It's just an example of automation done badly. Just have multiple QR codes to allow scanning in parallel. And if 6 people each paying for the own stuff creates a mess then sorry, that's just incredibly incompetent UX design. It should actually be easier to do it right when they're already ordering through separate devices!