> I assume the lowest-budget way to deal with a corpse in ancient Egypt is to toss it into the Nile.

So what, this didn't happen and isn't consistent with any historical practice. An irrelevant non-sequitur to the question at hand of whether pot burial is likely to be a poor commoner or even migrant worker or some representative of elite Egyptian society.

> that already disqualifies them from being poor.

No it does not, you're extrapolating way to much by way of some modern interpretation there's quite a lot of debate around these particular questions of provenance of remains that you're hand waving and trivializing as clear cut.