I think checkmates can factor into the timeout principle as is, while adding an added reason to avoid them.
You mate your opponent and they have to make a legal move. They cannot. So they must sit there for the remaining time trying to find a legal move. This excruciating waste of time is punishment for being mated. It makes it slightly worse to get mated than to lose on time.
The rule would logically also mean that a stalemate is now a checkmate. I would agree with this. If you put yourself in a position where you can't move that f@!# you and die King.
As a public service I'm developing a new form of chess for everyone who hates draws and/or can't understand why they don't win when they only have a King left and their opponent (with mating material available) runs out of time. I'm calling this great (sic) new game "Virtual Chess" so that people will equate it with other cool hi-tech stuff like computers, androids, unmanned drones, weapons of mass destruction and so on.
Virtual Chess is always played with a chess clock and can only be won by your opponent running out of time. Ergo, no stalemates or draws will be allowed. Thus, even if the players repeat the same position 3x or reach a state of perpetual check, they still keep on playing until someone runs out of time.
In case both players run out of time before either one notices they both lose. I'm still working on the rules to govern play when someone is checkmated before anyone runs out of time. One idea is to just keep on playing anyway and if one player runs out of pawns and pieces they get to put captured material back on the bd each turn so that the game can continue until someone exceeds the TL.
It's the wave of the future so don't waste my time with any whiny, sniveling complaints about what a stupid idea this is which will only show that you're too unenlightened to appreciate my 21st-Century, 64-bit, octocore digitally-enhanced and bio-enginered improvement to the long since worn out, dull boring and stupid version of chess that will soon be relegated to the obscurity it so richly deserves.
VIRTUAL CHESS: Coming soon (much too soon in fact) to a chess club near you! Be the first person on your block, cell block or padded cell to take part in this fun-filled, action-packed and totally tubular wave of the future! You'll be glad you did!
This offer is void where prohibited by Luddites or Emmanuel Goldstein.