The present file-tree does remember your place within files, after they have been opened for the first time. Adding tabs might make it slightly quicker to find the files that were already open. But unsaved files already have the filename in bold which - unless you are save very often - should help you find your way back to the file you were working on.
And, as Simon points out, this would cost vertical screen space. This is especially bad because the browser will (probably) already have a dedicated area for tabs. Then again, there are also some empty areas at the top right of the compiler: in the filename bar, and the menu bar.
It would be nice if the compiler could be tabbed so multiple files could be opened at once.
Sometimes when trying to refer to other library files or, even another example, it's a bit of pain to pull the the right file out of the tree, then scroll down to the part of the code your interested in, and then get back quickly to your code.