Without a dropbox login, syncing between devices wouldn't be possible (for this app). To sync you need some central storage online (which would probably involve some login) and dropbox has been a good resource for these kinds of applications. Wouldn't mind seeing a google drive integration though.
Even if you don't use multiple devices or browsers, browser databases are too mysterious for regular users -- too easy to accidentally delete along with history and too difficult maintain up-to-date backups of.
A better UI for bookmarks would be cool.
If it truly is client-side only, it won't strain resources to render the static files, so it doesn't really need a dropbox login-barrier.