in general, the answer is no...........a 2400 player must take a 2000 player or really any player seriously until he/she gets a clearcut advantage. And if the 2000 starts with White, the 2400 may never get an edge ! Tough to "crush" someone who has a strong basic knowledge of the fundamentals of chess.
Does a 2400 player crush a 2000 as easily as a 1600 crushes a 1200?

I'm not 2400 but I know the answer is no. A 2400 almost always beat 2000 but only if they take the game seriously

I would say it's the same pretty much ....
1600 rated player will surely crush 1200 player but he must show some skill , I don't think 1600 player can crush 1200 with an eye's closed , so if he concentrate's he can win quite easily, same thing goes for 2400 player 2000 shouldn't be a problem , if it's actual 2000 player and not some sandbager.

I would say it's the same pretty much ....
1600 rated player will surely crush 1200 player but he must show some skill , I don't think 1600 player can crush 1200 with an eye's closed , so if he concentrate's he can win quite easily, same thing goes for 2400 player 2000 shouldn't be a problem , if it's actual 2000 player and not some sandbager.
I've beaten an 1100 blindfolded so a 1600, that has been practicing blindfolded more than me, has the possibility of beating a 1200 blind

Does a 2400 player crush a 2000 as easily as a 1600 crushes a 1200? Is it as effortless win as it is for a 1600 rated player to play a 1200 ?
Yes, it’s just that the way he accumulated advantages is not as obvious to onlookers as the game between a 1600 and 1200.

Yes, a 2400 would crush a 2000 with relative ease.
A 400-point difference is a huge gap in both tactical awareness and positional understanding.
The same is true for a 2800 vs. a 2400.
Carlsen, for example, would mop the floor with any entry-level IM.

Does a 2400 player crush a 2000 as easily as a 1600 crushes a 1200? Is it as effortless win as it is for a 1600 rated player to play a 1200 ?
Yes.
Of course higher level games involve more technique, and the win may come on move 60 instead of 20, but over a 10 game match the results are expected to be the same because that's how the rating system works.
Does a 2400 player crush a 2000 as easily as a 1600 crushes a 1200? Is it as effortless win as it is for a 1600 rated player to play a 1200 ?
Yes.
Of course higher level games involve more technique, and the win may come on move 60 instead of 20, but the over a 10 game match the results are expected to be the same because that's how the rating system works.
I am always amazed when I think about how the difference between myself and a 500 rated player should theoretically be smaller than the difference between myself and the top players on here (3000).
Helps me put into perspective/semi-comprehend just how good the top players are

Does a 2400 player crush a 2000 as easily as a 1600 crushes a 1200? Is it as effortless win as it is for a 1600 rated player to play a 1200 ?
Yes.
Of course higher level games involve more technique, and the win may come on move 60 instead of 20, but the over a 10 game match the results are expected to be the same because that's how the rating system works.
I am always amazed when I think about how the difference between myself and a 500 rated player should theoretically be smaller than the difference between myself and the top players on here (3000).
Helps me put into perspective/semi-comprehend just how good the top players are
And if you take into consideration that it's harder to improve the further you go, you get quotes like (forgot who said it) that a 2600 GM is closer to 2100 level than world champion level.
Does a 2400 player crush a 2000 as easily as a 1600 crushes a 1200? Is it as effortless win as it is for a 1600 rated player to play a 1200 ?