Former World Champion GM Anatoly Karpov has lost a
match against Iranian GM Ghaem Maghami. The match was played in various time controls and resignation was not an option ... every game ended with checkmate.

Karpov was only narrowly beaten (1 full point) and that in the blitz round (the final available time control: 4 Min. + 2 Sec./Move).
Other than this match being a feather in the winner's cap the main point of the event was to promote this "no finishing until checkmate" rule. Is this rule practical? It seems that games that end in checkmate can be instructive but how can this rule be enforced? Couldn't a player sick of his position simply leave the tournament hall with his opponent waiting for the clock to run out? Is it better to leave the resignation rule and as long as you think there is hope ... you play on?
I think the rules are fine the way they are right now. resignation speeds up the whole process. playing to checkmate will add more stress on players, increase player no-shows (as players will feel more humiliated with each loss), and otherwise delay tournaments and tournament directors.
The conditions of Karpov's match were as follows: "The FIDE Laws of Chess were applied with the following exception: as a special condition, in respect to the public and the media, it was decided that all games should continue until the last playable move on the board. A player could not offer a draw or even resign the game. In a losing position a player had to continue until mate, and in a drawn position both players had to continue until a three-fold repetition of position, until lack of mating material for both sides, or until stalemate."
I can see where the rule would reduce the number of draws but I'd rather see the losers come back the next round rather than being demoralized in obviously lost positions. A director/organizer has to consider this when thinking about this rule. Then again maybe I'm missing something?