Well for that specific case, you'd need your Dad's passcode to install the enterprise cert. But "Facebook Research" is a thing that happened.
I think there's more that could be done to make the process unappealing. What if the setting erased all data on the phone, a la unlocking the bootloader on Android? What if there was a one-week time delay before the setting took effect? What if you had to visit an Apple Store?
(I don't like that last option, because it makes research inaccessible to e.g. people in countries without Apple Stores. But it would be better than what we have now.)