Allow me to indulge my chess fantasies

I crafted this position after a long double-round day, and was determined to create a novel puzzle. Please have a go: black to play and force a draw (answer below).
Answer:
Ok, I cheated a little bit. Well... not really. As you would have no doubt figured out, Black has one legal move: g2 checkmate. So how does Black create a draw?
Black should let his flag fall, that is, he should run out of time. Let me explain.
At a glance it would appear that White would win because he has checkmating material (a rook), but this is not the case. The FIDE rules stipulate that there must be a legal sequence of moves that will result in checkmate. In this case, there is no such legal sequence (where White can checkmate Black), because Black's only legal move is to deliver checkmate. In which case, the game is declared a draw.
BUT...
I would like to pose an interesting question to the reader. Should Black win this game, even though he has lost on time?
I know it might not make much sense, but hear me out. If the ONLY possible sequence of moves results in the victory of Black; why should the game be declared otherwise? It must be noted that there is always an assumption that the game will continue. For example, if a position has repeated three times, it is assumed that it will keep repeating until the players agree a draw. In the above position, we must part with this assumption... the game cannot continue as White would lose. And White cannot lose in such a situation. This is a fundamental problem. It is hard to say. Perhaps, the game is declared a draw to punish Black for his poor time management?
Anyways, this was just a fleeting thought.
Thank you for reading,
Real_Sp00f
P.S.
See if you can find what is 'wrong' about the following position. And yes I watched a Madonna music video and looked at the chess position. <3