I guess another feature could be that the winner is only obliged to play the second game if the loser actually requests the rematch. If there's no request, the winner gets the win and points as usual.
I suggest adding option to agree to 2 games in a row, one white one black

Otherwise the system could just be smart enough, or set a user option or setting... to "always choose opposite color for same player during next game."
That effect might only go into effect if the other playwe has it enabled as well, I haven't thought out all of the logistics.
At a basic level it would allow each player combo to consistently rotate colors.
I know a lot of players don't care about this and almost never accept rematch, but there are also quite a few like me, maybe a lot who do want the option to rematch (especiallly in certain types of games - like if you made a stupid blunder in 1st game, or you had a big lead but the oppo managed to stall you and time you out, or a loss because of a keyboard error).
Otherwise the system could just be smart enough, or set a user option or setting... to "always choose opposite color for same player during next game."
That effect might only go into effect if the other playwe has it enabled as well, I haven't thought out all of the logistics.
At a basic level it would allow each player combo to consistently rotate colors.
Now that I've thought about this more....
What chess club or meetup have you ever known where 2 players only play one game without the option for loser to play again in opposite color??
It's so basic that to not have it (choosing a pair of games as described in the op) on the biggest online chess site in the world is actually quite negligent and amateurish.
It's understandable that chess.com doesn't have it because maybe no-one thought of doing it yet.
But now that I've pointed it out there's no excuse.

i like the idea, but what if youre in a hurry, forget you have it on and have to resign game #2 because they dont have time
i like the idea, but what if youre in a hurry, forget you have it on and have to resign game #2 because they dont have time
That would be the same with any game wouldn't it? If something comes up you have to do, you might ask the opponent to give you a draw but usuallly they won't so you lose. in this double game scenario if yhou won the first game it ends up 1 each, if you lost you might go down 2 but the opponent might be mreo leiniet and give yhou the draw having won the first one.
anyway that's an issue in single games too so I dont see it as a deal breaker. when you take the option to play a set of 2, you know there's that risk so you don't have to take the risk if you don't want to.
i like the idea, but what if youre in a hurry, forget you have it on and have to resign game #2 because they dont have time
You could also choose "casual" double game if don't want to risk points.

- If the winner of the first game refuses the rematch, they get no win recorded (or maybe even get a loss) and no points, likewise the loser does not lose any points.
- But the loser of first game does not have to agree to rematch, in which case it is scored like a normal game..
What would be the point of that? This bizarre double standard doesn't make any sense.
Under those circumstances no one in their right mind would choose this double game feature. And those who accept it by carelessness would be unhappy when they are scammed out of their win.
This whole thing goes against the spirit of fair play and the spirit of chess.
This is a more fair and complete game because white is of course an advantage for most players.
How it could work:
2 players choose to play a double game...
- If the winner of the first game refuses the rematch, they get no win recorded (or maybe even get a loss) and no points, likewise the loser does not lose any points.
- But the loser of first game does not have to agree to rematch, in which case it is scored like a normal game. This is fair because they are not gaining from the refusal, and also they may decide they were outclassed and there's no point in playing again and just concede the one game.
Personally, my main reason for this is if I lose a close game I want to have the option of a rematch, it seems the fair and sporting thing. I know no-one is obliged to rematch but this option is for those who prefer to have the option of trying to redeem themselves, which currently does not exist.
Also if I win and someone wants to rematch after losing, I ALWAYS accept even if I don't want to, so this puts me at a disadvantage compared to those who refuse to rematch.