One issue that jumps out at me is if the system is air-gapped, how does the malicious software get there in the first place without being detected?
The malware needs to be deployed via existing trusted means of data transfer so you need to understand what that trust model is and search for weaknesses you may exploit. Is data transfer as simple as plugging in a USB stick or are there multiple gating functions like signature verification, etc on adjacent systems before you can move to the primary?
The data transfer is usually executed by a human being who must plug in some media with your malware on it either wittingly or unwittingly. The former requires working that human as an asset over a long term blackmail or HUMINT campaign. The latter involves compromising the supply chain that ends with executables being copied to the media vector.
These are concentric circles of controls between you and that airgap - but each has a weakness. There are entire agencies and organizations who live, breath, and execute targeted searches for those weaknesses. So yes, in my opinion these are real threats IF an adversary that has the capability, time, and funding to perform the above falls within your organization's threat model.
1. USB devices. If you need to move software from outside the air gap to inside, it's pretty easy to imagine somebody copying malicious software unintentionally through that. You might think that typical AV could detect it, but that could either be worked around, disabled by the operators of those systems, or simply not up-to-date because they're in the air gap.
2. Sometimes, air-gapped systems still have some kind of tunnel that allows an exceptional connection between a system outside the air gap. If you knew how to access that tunnel, you could effectively compromise the air gapped network.
I'm sure there are more ways too. But those are a few I know off-hand.
And sneakernet (floppies back then) was the primary delivery medium for computer viruses before it was common for personal computers to have internet access.
"Banks regularly use Faraday-shielded rooms to protect servers."
But they do not seem to be air gapped, as then the use of the data would be very limited.
I would assume, the main interest in air gapped systems are top secret, high value research projects, as well as many secret agencies, who must assume, that their IT equipment comes with a backdoor installed at hardware level.
Other ways of getting the virus in: at some point, the computer needs software and data. When the data comes in, so can a virus and uae a unknown zero day exploit.
[1] Stuxnet had compromised airgapped computers
USB pendrives, https://en.m.wikipedia.org/wiki/Stuxnet