What prevent a smartphone wallet from downloading my keys Wallet software use variant technologies to protect and hide our private keys like mnemonic or simply using the private keys.

What would prevent them from making a patch to their software that will install a keylogger, making a screenshoot, or simply going into the memory and retrieving those private informations ?
Nothing.

A Bitcoin wallet that is online and connected in some way to the Internet is referred to as hot wallet.

That is why it is recommended to keep as much money as you would put in your pocket in a hot wallet.