Show me one financial institution in the US that allows this.
I have cashed cashier's checks of up to about $30,000 at a local financial institution. It took a few minutes of them talking amongst themselves, a few more minutes to count it out in $100 bills (three times), and it made my bi-fold wallet very difficult to stuff into the leg-pocket of my cargo pants (which is an absurd thing to be doing, but I did it anyway). None of this attention to detail seemed inappropriate, so I count the result as definitely being "on demand."
The institution is Fifth Third Bank. Not that I recommend them for anything in particular because they've shown themselves to be incompetent in other ways that are important to me, but they had assets on-hand to deliver the amount within short order and without any sort of appointment.
*shrug* If the issue is whether or not any financial institution has large quantities of cash on-hand (for various definitions of "large"), I can say: Yes. No problem. (For me. So far.)