Another roadblock that I've encountered is moving a tab between profiles. For a multitude of reasons, foremost between them research, I would often come across a tab that I know would be useful for one of my other research subjects. If the profile in question is closed, there is too much friction to open it, copy the url, paste into a new tab, then close the profile again.

A single "Send to profile" option would be such a boon to productivity.