If you show productivity, banks have no problem lending you money (new freshly printed money)

Indeed, although there are also pressures pushing banks to lend out money regardless of created wealth. This is why there's so much investment into stupid things like AI - they call it TINA or "There Is No Alternative" (to put your dollars into). The scale of AI is as big as it is because there were huge pools of money sloshing around looking for things to invest into, that's the underlying problem that caused the RAM crisis, not AI itself.