Cold storage devices, or hardware wallets as it's often referred to, are used to store crypto coins, and not seed phrases or private keys, or maybe I am wrong, then I am ready to take corrections from another user that know better.
But over all, I agree with you @op, but then, I still believe that the safest way to store seed phrases is simply do write them down and keep somewhere safe, yeah, it might be in danger of water or fire destruction, but I believe this is why we are often adviced to make or create different copies of the same seed phrase and keep them in different places, so if paradventure, water or fire destroys one or two of the seed, we can fall back to the other backups.
Overall, seed phrases, private keys, are the number one things to give 100 percent attention to, for without them, we own no crypto, and if we hustle, gather alot of crypto for our future use, and someone, we let a possible scammer into our wallet seed phrase or private key, it simply means that all we have suffered to get, we might have suffered to get it for someone else.
So, yeah, it's of atmost important that we must keep safe, and protect our seed phrases, or private keys at all cost, employing different safety measures that are safe, to ensure that what is ours today, does not become someone else's tomorrow.
Btw, +1 for bringing up this topic.