~snip~
With my hardware wallet I have to connect it to my computer and unlock it to be able to pay.
An airgapped device can be reconnected to the Internet and you can propagate a transaction in seconds. The difference is that instead of connecting a wallet to your computer you're connecting the computer to the network for a few seconds.
You misunderstand air-gapped wallets because they never come into direct contact with the internet. If you have a cold/air-gapped wallet installed on an offline computer and a watch-only version on an online computer, then you will sign the transaction on the offline computer and transfer it to the online computer via USB/SD card and broadcast it.
If you have an air-gapped hardware wallet, then you will do the same in a slightly easier way, because you will
"transfer" the signed transaction to an online computer by simply scanning the QR code or using an SD card. You will even install the firmware via an SD card, so the device containing the private keys will never have access to the internet.
Air-gapped wallets are actually not complicated at all and I recommend them to everyone who has cryptocurrencies of a higher value.