They aren't mutually exclusive. The cutesy message also provides useful information (this is our fault, unintended behavior etc). Why not have both?

The thing is, cutesiness does not convey anything either useful or specific, and, as this discussion uncontrovertibly shows, may be taken in unintended ways, including as being patronizingly dismissive. This is hardly surprising, as the context in which the error occurs cannot be known to the message's author. One's reaction is immediate and visceral, even if, on reflection, it probably was not intended that way (though I have known one or two developers who always blamed anyone but themselves, and particularly users, for errors.)

I feel like this is unfortunately a semantic difference only - "cutesy" means different things to different people. Cutesy can just mean "informative but written in a friendly manner" to some people while as you and I understand it to mean "Jovial but unhelpful" - I think the user you're replying to is interpreting it in the first manner. A good example of a "good cutesy" error message might be Chrome's No Internet screen: "It looks like you don't have any internet, here are some ways you might be able to resolve it... but also here's a little dinosaur jumping game to pass the time".

Regardless of whether one might call such a response as being “cutesy”, it’s not the sort of response we are discussing here. The problem with the cutesy messages being discussed here is not that they are cutesy per se, but that their cutesy aspect is uninformative and quite possibly annoying.