It's so you can leave debug symbols in your executable: for a release you'll strip your binaries and pack them quite tight. For developing you'd like to have more uncompressed data in ram, and you want full debug symbols and debug info on the stack. Not to mention that debuggers themselves take a non-zero amount of ram.

Having more powerful hardware allows you to focus on designing/building the game and delay optimization until the game is mostly finished.

There is no reason to work under tighter constraints. You want developers to be able to push the retail version of the hardware to the limits. In order to do that and still be able to run debug builds you need the dev kit to be more powerful than the retail version.

I think that having the same hardware would be logic, but I feel that running (especially a game) in debug mode would in fact require more memory...

I can see using the same specs, but using even less would be weird. You don't win any points if you use less memory than the hardware has.