It's simultaneously overblown and under blown

People are paranoid about hot wallets because they have too much hot, which is under paranoid because there's too much there in the first place.

A lightning node is inherently hot. A cold storage node not necessarily, you can do the node functions like mempool etc without a wallet ... Then attach a cold wallet to it like it's a database on a private network.

Having a key accessible to the iternet is what makes it hot, you might have Core behind a double firewall or proxy node such that it's wallet is not hot.