Whether that's crazy depends on your threat model. If there's no reason, it could still be crazy in the sense of protecting from an irrational fear. If you communicate with people or organisations who shouldn't know your location, it makes sense. It depends

If you've ever been stalked by a crazy ex-girlfriend who is from a very rich family, you'll probably feel a little "paranoid" or whatever.

I was already on the "I just want to be left alone" vibe generally before all that happened to me, so I just carried on as usual.