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My employment requires personal phones to have its cameras destroyed or completely removed for security purposes. Will an iPhone 12 continue to function normally (with Face ID off) even if all cameras are removed?

Why would your employment require you to destroy your personal property? Can you just not use it during work or block the cameras with tape? Apple really hates things to be not present on their devices, usually their software won’t stop asking for things that are supposed to be there, this at minimum causes the software to loop all the time and drains battery, worst case scenario it won’t even boot. As for this specific scenario, I have not tested it.