Is there a reason why double-clicking on a text component doesn't automatically put me in text-edit mode? It seems unintuitive to have to go click on the little pencil button to get into text-edit mode.

Because double-click takes you to the Properties Tab. When you add an element, 99% of the time you are going to want to change some sort of style long before you want to change the text. That is why you go there by default. From the Properties Tab you can click the icon to edit text.

Tripple-click however is reserved for editing text if you want the shortcut.

But, I'm not adding an element, I'm modifying an existing one. As far as I can tell, single-click also takes me to the Properties tab, so it would be no big loss of functionality to make a double click take me into text-edit mode. It would also be nice to be able to resize an image by double-clicking and then dragging the edges to the size I want.

Please don't get me wrong, this is a great product! But you asked for suggestions to improve it. My idea of "improve" may not be the same as yours, but I thought it worth offering my suggestion(s) anyway.