How do you propose you would get them back? By clicking on the appropriate icon (in the case of stats window, inventory, etc)? The alternative being they fade out so you can see through them, but remain there so you can get them back by simply mousing over the area where they were... but I suppose that could get annoying.
So basically the windows would toggle off after a set time of inactivity, and then toggle back on when activated.
I think its a good idea, because the interface does really get very cluttered at the moment.