This would be an epic add-on. The ability to log into one's website or other's and work within ClickUp would be super-ideal. Actually, all things considered having some kind of Wordpress ClickUp plugin which allows login to the web from ClickUp + post creation a task or a Doc as an integration would be extra-cool.

This would be fantastic to have for individual clients that want to see updates on things - they log in to see their dashboard, but it's from a personal site! This would be fantastic as it is not jarring to switch to another page to see their data.

White labelling could function the same as it does now with the Enterprise plan, where the login can be branded if the workspace pays for it.

This would be amazing, in addition to have some basic controls of the embed view - for example: Make it so you can force the side menu within an embedded Doc view to stay OPEN. We use embedded docs for a knowledge base and it's shocking how many employees can't figure out where the menu button is... even though the first thing our Doc says is "USE THE MENU BUTTON IN THE UPPER LEFTHAND CORNER" and includes a GIF recording of a cursor clicking on it. Having a layer of authentication though like you said would also be just an amazing feature add for personal sites so these things are easier to manage permissions on!