If you use a dedicated smart phone (factory reset and everything) or a dedicated laptop / pc (fresh install, not used for anything else) you should be fairly safe, that's true. I'd still go for a hardware wallet however. They don't cost that much and keep your coins safe even if physically accessed.
Disagree I don't think mobile wallets are that safe even if you take those precautions. The only wallets I feel safe with are hardware wallets or paper wallets because those are never online but rather offline completely.
To use bitcoin then an internet connection is a must, don't you know that basic? Bitcoin is a digital currency in the first place.
You don't need your wallet to be online to store Bitcoins, only to sign transactions. Using hardware wallets or paper wallets enables you to store your Bitcoins without having the respective private keys exposed to the internet.
In the end you still need internet connection to use your bitcoin.