I find it helpful to assume an adversarial worldview to any service that collects or handles data. You've mentioned some reasonable assumptions about how this

I find it helpful to assume an adversarial worldview to any service that collects or handles data. You've mentioned some reasonable assumptions about how this system might work. But it's ultimately trust in a black box and a manufacturer with whom you have no personal or business relationship. You have no way of knowing if, at any time, your assumptions are still correct, or if one day in the future what's inside the box gets changed out. What incentives would it take for that to happen? To my imagination, not much. E.g. the manufacturer thinks it can start a side business collecting and selling your full prints. There is certainly a market for them, so why not collect them? Maybe law enforcement sees these devices proliferating and convinces lawmakers to require that the prints be stored to support local investigations. Who would be against catching predators at your gym? Meanwhile the gym doesn't care because this isn't it's problem---and it gets a discount. Things can change fast. If it seems possible, someone is probably thinking about how to do it.