But one important attack vector is the online machine it is used with. While in theory there shouldn't be any way to compromise the device from an online pc, this shouldn't be completely ignored.
Especially phishing attacks can work pretty well. And a vulnerability in the microcontroller and/or secure element can make the hardware wallet insecure when used with a compromised PC (which it is made for).
This attack vector only applies to hardware wallets, but not to air-gapped wallets.
I wouldn't consider a hardware wallet as secure as an air-gapped wallet solution.
Deifinitely, I won't consider anything impossible when it comes to security. If the attacker can compromise the hardware wallet with a vulnerability in a secure element and without physical access, then it would be terrible. I hope that it wouldn't happen and it's probably why some hardware wallets are able to be run with an airgap as well. If that's the concern, then I guess that'll make it more equal.
Some APTs and malwares has demonstrated their ability to jump airgaps. Definitely possible and has been done but it's quite a lot of work, would've been easier to just compromise the OS itself. What I think could be a potential concern other than the sidechannel (I've mentioned that enough and I know secp256k1 mitigates some of it), is that despite the ability to encrypt the files, which should be viewed as a workaround other than a mitigation, there isn't any way to ensure that the files cannot be extracted from the device, I believe you can clone the HDD/SD card to try it again and again. As you've mentioned, the seeds are stored within the secure element and X failed attempts would brick it and render it unrecoverable in some HW wallets.