Not commenting on GP's point but... No, you don't.

You can prepare your transaction on an online machine, without signing it. With full access to the blockchain, the balance of every address, the "counter" needed so that you tx is legal (in Ethereum's case), which address you want to spend from etc.

Then you transfer that transaction, without using the Internet, to the offline computer and sign it there and transfer the transaction back to the online computer to broadcast it.

The computer preparing the transaction, the one signing the transaction and the one broadcasting it can be three different computers.

You can even do that with an hardware wallet: the hardware wallet does not need to be plugged to a computer that is online. It can be plugged to a computer that is offline.

There are still many issues, even when using airgrapped computers. For example it's possible that a hardware wallet vendor is using non-determinism in "random" parameters chosen to sign transactions to exfiltrate the seed hidden among signed transactions. So even an offline/airgapped computer and a hardware wallet hooked to that offline/airgapped computer wouldn't help.