I'm guessing that you have a relatively low resolution display then! Mine are mostly at least 1920x1080 pixels native (1280x720 after High DPI scaling if enabled) and often considerably bigger, and given that the default BBC BASIC window size is 640x500 (and I virtually never go bigger than MODE 20 which is 800x600) there's almost always room for both the IDE and the output window with only a small overlap.
But of course if it's a spreadsheet or slideshow style application then it's entirely reasonable to want to run your program 'maximized'. However even then you ought to be able to 'restore down' to a windowed mode if that helps with debugging (or for any other reason such as dragging-and-dropping data between windows).
This is one reason why it's a very bad idea to set your window size to the size of the screen, or to use a MODE which is nearly the size of the screen, because then you have nothing to 'restore down' to! Far better to set your nominal window size to something significantly smaller than the screen, but to switch to maximized state most of the time (either using an API call or when you 'compile' your program).
If clicking on the title bar button to toggle between 'maximize' and 'restore down' states has little effect, because you've set the window nearly to full-screen size anyway, you're defeating a valuable feature of the Windows GUI, which is obviously undesirable.