Why did they leave the port at all?

Because I can't imagine people are happy to pay to sit for a week in an industrial dock in Portsmouth. Also sailing to warmer waters means you can sit on the outside deck/balcony and enjoy the sun. Again, not exactly the things UK ports are well known for.

I'm going to guess that there are laws that make that pretty undesirable. For example: There were (and maybe still are) gambling ships on the Ohio river and on Lake Michigan - all of which docked in Indiana. Unfortunately, such gambling was illegal in Indiana. The ships had to leave dock and go out a little on the water. Suddenly, the gambling was legal.

There are probably dozens of these laws that encourage leaving the dock, especially if you are going into international waters instead of simply between states.

Yes, the LA to Las Vegas gambling air cruiser would be a profitable route. Sunsets would be fantastic!