You increase your risk when using a paper wallet versus using a wallet stored digitally. Regardless of how the private keys are stored, you have a set of risks when creating a private key on a computer. When you move that private key from your computer to paper, you have to incur additional risks.
And there are additional risks you incur when you store private keys long term on digital storage rather than on paper or some other physical medium. Hardware degradation is one, as I have mentioned above. You can choose fireproof paper or laminate it to protect against mild water damage, which could destroy digital storage. The risks of accidentally exposing a digitally stored wallet to the internet is much greater (plugging in the wrong USB drive or CD to an internet enabled device, leaking data between your airgapped and non-airgapped computers) than a paper wallet.
You can use a paper wallet as a backup to address the issue of hardware degradation (you should keep your private keys in at least two mediums of storage for this reason).
Accidentally exposing private keys to an internet-connected device does increase risk, but does not guarantee loss of funds, and if this happens, it is a sign of carelessness. On the topic of carelessness, if you accidentally show someone your paper wallet, the risk of loss of funds is much higher because they could take a picture of the paper in seconds without having prior intent to steal your funds. Exposing private keys to an internet-connected device requires the device to be previously compromised to result in a loss of funds.
There is also the issue of transferring your paper wallet private keys back onto a computer when you are ready to spend your bitcoin. This will require one to potentially allow a camera to take a picture of the private key -- precautions can be taken to reduce this risk, but the risk is still there. If you store your private keys digitally, there is no risk that taking out a USB stick will result in a camera being able to copy the private key. You have the same risk of leaking data between your air-gapped and non-air-gapped devices regardless of if you are using a paper wallet or storing your keys digitally. (you should really not be using your air-gapped device for anything except for signing messages/transactions).