It's not a difficult answer—I bring a burner phone with me when traveling internationally because I don't want to run any risk of a thief getting the keys to the kingdom. Sure, I could remote wipe if that happened, but it feels a lot safer to just not have a phone with real data on it at all.
You're not the first person they've detained who didn't want to bring their real phone with them for totally innocent reasons.
You're not the first person they've detained who didn't want to bring their real phone with them for totally innocent reasons.