So unless an extension can use local storage or encryption, I don't think it's going to happen.
It's definitely possible, several extension (such as MetaMask) use those feature. The real question is, are there any contributor willing to add and maintain such feature?
The local storage is probably not a problem. Just the notes will not be synced between multiple devices.
I also agree that since it's a feature with a rather limited use case, there may not be anybody willing to implement (and maintain) it.
If OP really wants to save info into browser, maybe a Firefox extension like Very Simple Notepad could help, although I'd prefer a proper local text file.