It isn't hard. You either use a cookie or, best for modern browsers, localstorage.
There is a clear API for using localstorage which you should be able to use via a Dashboard template node. Basically, localstorage gives you a key/value store associated with your URL so you can stuff things in it and retrieve them when you like. It is automatically persisted to disk so you don't have to worry about it. It is exactly what you need for persisting browser settings.
That would require everyone using the node to also use Dropbox. That is not a good user experience. Not everyone wants to sign up to cloud services, not everyone wants to or even is permitted to connect their Node-RED or browser to Dropbox.
Perhaps not, but the Node-RED server has to have the Dropbox credentials and a connection to Dropbox both of which could also be security issues for some. Not to mention that many corporate/enterprise firewalls block access to Dropbox and similar services.
