The plan I think is that the new cars generate a lot more downforce from ground-effect, through carefully shaped channels on the base. This means that when they get close behind another car, they still keep most of the downforce, whereas a current car relying on barge boards etc loses a lot when right behind another car.
So in theory, yes, cars should be able to follow more closely without losing downforce... which should lead to better, closer racing, and more overtaking.
But yes, you'd still expect to see Mercedes first, followed by Red Bull. I think a lot of the Mercedes problems this year were due to how the changes affected high-rake and low-rake cars differently, which caught them out... so 2021 gave other teams a chance. Next year they could well be ahead again.
The dirty air thing was the most important part, when cars followed each other there were two different approaches, one is being right behind them, like literally right behind them and that would give you a chance to close up and be ahead in a turn or two, or you would be like maybe one second or more further behind and that would give you dirty air, basically just a car flew right by that place a second ago so you know how it feels as well, and that made cars not have the grip they normally have.
This is one of the reasons why cars are much faster in quali then the race most of the time (along with many other stuff like fuel load). So with these new cars, if you are 1 to 3-4 seconds behind, the car in the front won't slow you down, and you will have a better grip on the car and a better downforce when you turn and all of that equals to cars getting inches closer each second they race.