What makes you think there’s no way of updating the firmware?
I don't know, but the amount of USB drives I've seen with a readily identifiable serial or jtag port and API documentation is exactly zero. 😉
I think most of them were one-and-done, as in, code/hardware was designed once, and never iterated on again, at least not for devices already in the field.
If every time an OS had to delete something it had to fill the space with zeros or garbage data multiple times just to make extra sure it's gone, we'd all be trashing our flash chips very fast, and performance would be heavily degraded. There really isn't a way around this.
The solution to keep private files private is to put them into an encrypted container of some sort where you control the keys.