The part where Enpass servers retrieve the icon is clear.
What you, nor any documentation, doesn't mention is exactly WHERE are the icons stored at. If on my vault, it's more then strange for the icons not to stay on at the point where I uncheck the "use website icons" checkbox. If at Enpass, that's a clear breach of my own rules for privacy and I won't use that feature no matter how much it would increase my usability.
I'm speculating here:
Website icons are stored in my vault, but you botched the implementation. There are actually two operations hidden into a single checkbox: 1) Use, as in display and 2) Fetch.
For this feature to be useful, I would love to use the icons, but not to automatically get all of them (I have hundreds of entries in my vaults). To balance usability vs. privacy, I'd love to manually specify which icons should be loaded. Does this make any sense?