Why doesn't the Windows command prompt window maximize to the full screen size?

"The reason is that the command prompt is owned by a specific subsystem (csrss.exe) in the windows architecture which is different from the normal Windows subsystem (win32k.sys). Because of this, command prompt windows behave differently then normal windows. You'll note that amongst other annoying behavior, that setting properties for a prompt will only apply to prompts launched via whatever method that particular prompt was launched with.

Why this is, I have no earthly idea."

"You can press Alt + Enter to toggle full screen.

Edit: This applies only to Windows XP and earlier. This information is five years old.

Edit again: This also applies to Windows 10. The previous edit is now five years old. How long can I keep the chain alive?"

Here the ALT+ENTER fullscreen has returned in Windows 10. But in Windows Vista and 7 you can't do that. For that you need display drivers from Windows XP. But if you do that you will lose Aero and stunning GPU effects. That will be a terrible idea so do at your own Risk. BTW I use ConEmu much, it can go fullscreen.

You can try DOSBox to make cmd.exe go full screen.