Think of the label text box with its leader as a special sort of group. If you double click on the text in the label you can edit the text just like you can with a regular text block. As you found, double clicking on the leader allows you to access the text box without opening it to edit the text inside. Then, just as with a regular text block, you can resize it.
What is it you’re putting in the label text that makes you want to avoid using Enter. I would rather determine exactly where I line ends in the label or in any text block using Enter instead of resizing the text box.