I mean more the "Why don't you ..." It's quite obvious that it's rethorical but it seems so nonsensical to put this into a question while camouflaging what is really going on.
As others have said, it's definitely a 'softening' of a request to make it more polite ('Go home' vs 'Would it be possible for you to go home?').
But I think there are some status games going on here, too. A subordinate would never use that phrasing with a superior.
While the phrase uses conditional language to 'soften' the request, it's also an imperative (an order) that's made to look like a request.
Try to imagine the boss saying this. How would they have said it - with an upward inflection at the end, as in a question like this one? Definitely not! The phrase would definitely end on a downward inflection, as in an order like 'Please go home'.
It's a curious turn of phrase that I'd suggest is particular to managers, parents, and other authority figures that need to maintain a veneer of respect for their subordinates. It also strikes me as uniquely American; I couldn't imagine a Brit or an Australian saying something like this (but happy to be corrected).
"Hey, bud. Why don't you pick up those two plastic containers and follow me."
"OK, but dad, it really confuses me when you say that. Can't you just say 'please pick up those containers'? It sounds like you're giving me an option but you're really not."
Until he said that, I had never given it a thought. But he takes things very literally, so I can see how it's confusing even though he knows what I mean.
I think English littered with these suggestive polite negation statements.
https://en.wikipedia.org/wiki/%C2%BFPor_qu%C3%A9_no_te_calla...
(I don't know whether it has exactly the same set of connotations in Spanish as in English, but it doesn't seem like the king expected Chavez to do something other than comply.)
Both people presumably do know what's really happening, and this is exactly why it's seen as unnecessary (and inconsiderate) to actually say it. There's no reason to call extra attention to something unpleasant.