Then why haven't they reported any profits using GAAP (generally accepted accounting principles)? They all use ARR which is easily gamed.

They aren't profitable on a GAAP basis and no one claims this. This obsession over profits is misguided. These are hyper growth companies growing at a scale never seen before. It is both deliberate and uncontroversial to invest in growth rather than slowing down to produce profits.

If my retirement money is going to end up invested in these companies, either directly when they IPO or indirectly through compute providers, then I would like to see some proof that they are capable of producing profits. "Trust me bro" just ain't gonna cut it.

I don't really sure, but might be they count hardware purchase as loss, too.

Google has just recently upgraded their TPUs.