Actually, the project browser is the list you are talking about

This is just a question of a different workflow. Because if it would work as you described, that what would be in this list box? In a complex model, there could be tons of classes. Then you have a tiny list box and you can scroll till the end of the day.
Then, eventually, you would want to use the project browser!
I don't really see the problem, if you create a new class diagram, the classes you would add are most likely in the same package. So you open that very package in project browser and drag all your classes onto the diagram. This is must faster or in your terms "simpler" than to use the context menu.
In case you don't know where the class is, you could use icon "Find in project browser" from the PB toolbar and enter the name of the class. That EA jumps immediately to the element and you can drag it on to the diagram.
If you want to see a flat view of your classes, right click on the model and then "Show Element List". Unfortunately, you can not float that window so you can not view this window AND your class diagram at the same time.