If you are talking to someone on the phone and say ‘I’m at home’, this not only indicates your location but also that you are able to talk without interference from traffic for example or other people with whom you might be working - you can have a private conversation.
If I may add a suggestion, I’d say “I am at home” is neutral, you simply tell someone where you are, but you would usually not say this to someone who is already there; you say “I am home” when you have just arrived, and you would usually say this to someone who was already there.