If You Could Change One Rule In Chess, What Would It Be?

Looks like checkmate the pawn is blocking the king to escaping to G8

Yes this is a checkmate, Black wins.

If the white king took the black rook, then black could capture white’s king first. Whoever’s king gets captured first loses.

tough one

in the Mechanics Institute they have a tournament where you have 1 round per Tuesday called the Tuesday Night Marathon (TNM) this rule would be helpful lol

Yes it is checkmate but which side of the disagreement are you on lindabell?
In live blitz tournaments - black could try playing KxR and then maybe claim 'Flag down' against white.
But when the Tournament Director comes over - he will see an illegal move on the board. Because the white King can't legally go to f8 there - not even capturing and not even capturing to get out of mate - and not even on Tuesdays.
The Director will go by the board position - not the clock - whenever there is a conflict between the two.
In live blitz tournaments - taking the King is often allowed.
So after Kxf8 black could go King takes King.
White: 'Your flag is down!'
Black: 'But I have your King. You lose.'
And indeed White Loses there.
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In slow chess tournaments over the board - do illegal moves lose?
Well you can't play King takes King.
If you touch a piece that can't move legally - then you don't have to move that piece.
That would include touching a piece other than one's King - when that King must move out of check.

If a player wants to be obnoxious he could keep touching his opponent's King.
The other player could complain and if the Director comes over and the offender keeps doing that - then the complainant might be awarded the full point with the offender forfeiting the game.
Some players will try to be as obnoxious as they can be.
The director needs to be wise to such players and ban them from both the tournaments and the playing areas.

The winner gets to take the chess set home.

In the position shown by Lindabell ...

black can also call 'Mate'!
And that's it.
Whatever white tries - to take the rook - to call flag - will not work because black has already called 'Mate!'.
If black has not called mate - but white has already called 'Flag' - then white still loses if black completed his move before white called 'flag'.
In other words if black let go of his rook at f8.
Black can actually call 'Mate' before he even begins the final checkmating move.
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Where/when might there be an Argument?
White calls 'Flag' before black has completed the mating move - or even started it.
The tournament director though - if he sees mate played on the board is likely to go by that.
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Opportunity for Cheating:
White calls Flag before black's flag actually falls. And before black has mated white.

in the Las Vegas Chess festival, thats what they do after the last round

but this rule won't work for some tournaments because most of them require the player bring the set and clock so it would be unfair

King can make pawn with queen 3 Times for one game.(Don't ask me why its so sus)

Hey what about 3-dimensional chess?

hmm... I propose a new piece in the middle at the beginning. The player who gains an advantage has the right to use. If advantage or score changes on favor for the opponent, opponent can command this piece and this way alternately. Now is born Double agent chess 😂

When I was a kid, I had a Star Fleet Technical Manual (I still have it; black vinyl jacket and all). I made a Spock-style tridimensional (apparently now called Tri D) set out of cardboard (using my own small plastic pieces) using that book. I don’t remember where I got the rules and starting positions, but I remember that I did not make them up. Bits of the board itself (the four small 2x2 boards) can even move during gameplay, which made my crude construction challenging.

I found the game bizarre and unplayable. It seemed highly contrived - how can we make 64 squares look futuristic for a TV prop (considering that Nemoy was not actually playing, of course, so the prop designers were not concerned with gameplay). It was not a game; it was a prop invented for the show.

Other variations (which pre-date ST:TNG) “stack” regular 64-square boards on top of each other. It is not really necessary to have these boards physically stacked; you can lay them beside each other just as well. I have never tried playing this way.

Out of curiosity, I checked Amazon just now. The only Spock-style 3D chess set I saw was a ST:TNG branded set. If this type of game were truly interesting and fun to play, you would see MANY variations available. But you do not see such variations, while seeing many regular boards, so 3D sets must not be as entertaining as regular boards or you would see more of them.

Here are the original Star Trek plans:

I would abolish the castling.

This would greatly simplify the rules - especially for people who are learning to play chess. Especially in terms of when you can and can't castle, but also the rule about repeating a position. Chess would be a bit more active because the king is more at risk. 
The castling rule came about very unwisely, as did the stalemate rule.

You can see in chess that the rules were created spontaneously. Unlike Japanese chess - shogi, where the rules were defined by the top players.

make the king stronger like why does he rule the nation he can move only a single square per turn hes an easy target give him like a buff so the game is harder but easier either i change that OR end chess racism instead of white first just do it random so sometimes black and white

it wont do anything to gameplay but removes a minor offensive detail

i would a new move better than brilliant move called divine move

Korean chess (and shogi and go) are really great because there is no draw in them. Of course, some version of chess without a draw would increase the popularity of chess.

Chess is perfect.

This thread could be retitled: given a chance, how would you like to damage chess?

The best way to damage chess and make nobody care would be to have everything be speed chess and no serious classical tournaments.