I hate the threefold repetition rule

Why?

It's an error to assume a relationship between 3-fold repetition and perpetual check. Repeating positions is just that and it happens with or without checks. Without a repetition rule the players will run into the 50-move draw rule (or the new 75-move automatic draw rule). FIDE decided that was still wasting too much time in its rated and recognized games and tournaments so they gave us the repetition tool to draw even quicker in many cases. Removing both the repetition and the 50/75 rules would hand the game completely to the trolls These would simply refuse all draw offers and play on forever or until clock time expires to anyone's (bad) luck . And without clock, you know what you would do to someone trolling you this way, do you? FIDE does approve!

The fundamental point is that by game theory all games must end if only to register the outcome and prevent algorithms from infinite looping. Therefore every proper game system should provide rules which guarantee that every game ends in one of the defined end positions. In chess, it's the 50/75-move and repetition rules which deliver guaranteed end positions. Or the clock as a last resort though dying of old age is probably not on the card

Note: perpetual check and repeating moves are old concepts no longer in the FIDE laws.

3 fold repetition, I see no reason to change that. But stalemate draw to me is "wrong". From a "chess is war" perspective, what is the reasoning for example in a KQQQ vs K endgame, an accidental  stalemate leading to draw? White is unnecessarily bullying black so black should be granted half a point?

At various times throughout the history of the game a stalemate has bee a win for the stalemating player, a loss for the stalemating player, or a draw.

The goal of the game is to checkmate the opponent. If a stalemate is achieved instead, that goal was failed and doesn't really deserve a win condition. If course, being stalemated doesn't either, so a draw seems like the best solution.

This is a great rule! But I think it needs some clarification.

- What if the dead player is revived?

- What if the player to move almost makes his move, so it is clear what he was going to do, and then both players die at the same time? You may object that he didn't complete his move, but exactly when is the move complete? And what if opponent when he dies falls and pushes a piece slightly out of place too (a push that would be an illegal move), so they both kind of but not completely messed up the game?

- Arguably, the player who won probably is dumb enough to start another game, and he will probably end in another infinite game. Is it not arguably a win for his opponent, who at least didn't have to keep playing another infinite moves game?

- In professional games, in all games now I think about it, what punishment is appropriate for players who in such a position refuse to play on until one player dies?

- If a player is about to die, but he has a kid, is he allowed to let his kid take over to keep the game infinite? If not, what if he donates so many of his own organs to his son that arguably the kid is more his father than he is himself?

- If the players play so long that they wear out the pieces so they completely disappear, and there is nothing left to move, does that count as a forfeit? How many atoms should be left of a piece for it to be considered still existing?

I of course know that what I said was just a matter of taste, and there are all kinds of ways to argue this matter. My taste still says what I said before.

But your taste doesn't say what you would replace it with.

This is a draw under the dead position rule whichever side is to move.

Would your taste dictate that the dead position rule were amended to:

5.2.2
The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king or stalemate the opponent with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.

or would you still class this as a draw?

If the former and it were White's move, would your taste dictate White wins because he stalemates Black or that Black wins because he has more material when the stalemate occurs? 

If the latter what system would you use to value the pieces in general positions and what would be the result if the material valuations were equal (e.g. after removing the b6 pawn in the above diagram)?

Obviously, it should be seen that the 3-move repetition rule is necessary. One might change it to four moves and that might cut out the majority of times when one player mistakenly allows a draw. I think perhaps that would be a bad idea, because players should know what they're doing and pay attention.

First of all, I am not used to this chat interface, what does this mean:

"Botlo thought should happen. Would it be just a senik wrote:" ?

Anyway, you bring up a good point. I suppose the easy way out would be to allow "pass" moves, and like in Go, double pass is draw. It fits the war narrative, you can do nothing in a war, but opponent may be doing all kinds of maneuvers while you do nothing, which may result in big trouble for you.

Yes indeed. I don't think it's possible to get used to this chat interface.

Your suggestion would seem to be the most natural. It would change the game less if you said a  player must make a legal move if and only if he has one. (Otherwise you wouldn't usually be able to win in KNNvKP or KPvK for example and only a player who is not winning would want to pass, so the game would be more drawish.) 

But I think the status quo is possibly more interesting to play.

"no no no, you're supposed to argue, 'ten for that you must be mad'"

https://www.youtube.com/watch?v=nwWz0VM94m8

I suppose I would be fine with a smaller rulechange, that says you have to move, even if you are in stalemate, or you lose, and if you make an illegal move (including one that leaves king in check) and opponent points it out, you also lose. You can of course just resign also. So in your example above, the player to play loses. There are other non-stalemate mirrored positions with the same outcome, and such stalemates are very uncommon, so I see no problem with such a rule.

Logically, it can't matter who has more material if neither side can move. You can't skip moves in chess, you have to make them and if you can't, it's a draw. You have no way to use your extra material. If someone were to win, should it be the side who made the last move or the side who didn't make the last move? There's no reason to prefer one to the other. I prefer that the side who didn't make the last move and therefore cannot move should win. It appeals more to my sense of aesthetics but that isn't a logically motivated reason.

I raised the question of material difference only because @Botlosenik started the debate with

what is the reasoning for example in a KQQQ vs K endgame, an accidental  stalemate leading to draw? White is unnecessarily bullying black so black should be granted half a point?

I agree material difference shouldn't come into the question.

One way to approach this issue is to consider the principles of fairness and sportsmanship in competitive games. In a fair game, the outcome should depend on the skill and strategy of the players rather than on arbitrary or questionable tactics. Allowing a player to repeatedly use cheap checks to force a draw undermines the integrity of the game and can be seen as a lack of sportsmanship.

From a mathematical and logical perspective, it is also important to consider the purpose and function of rules in a game. Rules are meant to create a structured and fair environment for competition, and any rule that detracts from this purpose should be carefully evaluated. In this case, the rule that allows a player to repeatedly use cheap checks to force a draw does not serve a useful purpose and may even undermine the overall fairness and enjoyment of the game.

The rule is problematic from both a fairness and sportsmanship perspective, as well as from a logical and mathematical perspective. It is  indeed a profoundly stupid rule that should be struck from the rule book. It has served no one and only shows Chess' issues. 

You say what you don't like, 

What to replace it? An extension of the dead position rule to include corpses at the table?

If a player opens themselves up to the possibility of a triple repetition of position or one where eventually 50 moves without captures or pawn moves happen (perpetual checking), then their skill was lacking in preventing that option. 

Players should always be allowed to play whatever legal moves are available and if the best line is repeating the position or continually checking, then that should be acceptable. 

The other player, if possible, may be free to deviate and stop repeating or block checks; however, that may be a losing proposition as well.

The player would not be lacking skill for "not seeing it". A bad rule is a bad rule.