Is there a specific reason to not gather the entropy from an electronic device?
You need to trust the software you're using. It's a lot more difficult to compromise a coin flip than it is to compromise a recently sold paper wallet website.
You have to trust software to spend your coin when you spend it. When you sign a message or transaction, you combine what should be a random value with your private key to generate the signature. If you know one, it is trivial to calculate the other with a given signature. Malicious software could possibly leak information via this random value.
Creating a kay "by hand" also has a greater potential to make mistakes.