New Draw Scenario

Idea for new draw scenario: If you can, in 1 move respond to checkmate WITH checkmate, the game is a draw. Example: (and I don't know how to imbed a board in a post, so if anyone sees this and wants to either teach me or make this setup that'd be neat) White king on h1, black king on h8 both sides g and h pawns on starting squares, white rook on b2, black rook on a7, white to play. Rb8 is mate, but with this change black can save a draw with Ra1. I hear you asking "OP... why?" "because my inquisitive friend-" I'll answer. The basic "lore" of chess is two armies fighting to vanquish the opposing king, however if both kings on our hypothetical battlefield have a sword to their respective throats, I imagine they'd call it a draw. What do you think?

Technically the goal is to capture the king. With your rule, I could respond to your check with a check of my own, and you could choose to make a draw, or play on. Our kings are about to die,
but if one dies the other will too.

I like, whoever captures the king FIRST wins.

Why would you want to add more draw conditions to chess?

Arguably it's too drawish as it is; that's why many varients reduce the drawing capabilites. (e.g. KoTH, any varient where you try to capture the king)