Controlling and occupying

Occupying the center is almost always good... for any piece. Even the king and queen. In fact in the endgame getting your king to the center first can be a big advantage!

But early in the game there are a lot of pawns, bishops, and knights on the board. A king will of course get checkmated if it tried to go to the center early, but a bishop would likely get chased away. Pieces of lesser value can (almost) always chase away a piece of greater value. So a bishop in the middle (or queen, or king) is likely to be a liability early in the game.

Knights and pawns do the best in the center. Pawns because no one can chase them away, and knights when they're on outposts. Even though knights and bishops are worth the same, the nice thing about a knight in the center early in the game is it can't be blocked (because it can hop over pieces). Early in the game when both players still have most of their pieces and pawns this is a factor that makes knights stand out. Later in the game, when the board is fairly empty, bishops tend to outperform knights because they can quickly go to any part of the board.

Put any piece in the center of the board, and count how many squares it can move to.  

Now take those same pieces and put them somewhere away from the center, and count how many squares they can move to.

Or... if that doesn't answer you question...

The opening focuses on control instead of occupation because in the beginning both sides' forces are disorganized and far away from each other. The player who brings more troops to the battle will win so to speak. So first the players try to get all the knights and bishops off their home squares, then later, sure, you occupy anywhere you think is useful... and as bacon points out the center is pretty useful because you can control a lot of squares there (vs a corner or edge).

A  pawn that occupies a center squares is worth 2 points.  

A  pawn that controls a center square is worth 1 point.

That's seems a little extreme.

For example you're saying sacing a knight for two center pawns would put you ahead in almost any position.

Sure such a sac would usually give a fair amount of compensation, but outright better?

And especially in the opening, losing a piece can be worth even more than 3 pawns.

https://www.danheisman.com/evaluation-of-material-imbalances.html

(see section "BISHOP or KNIGHT VS. 3 PAWNS")

The formula im using is strictly to figure out center control with the pawns.  The point value used is not in relation to traditional chess piece values.

You have asked an old and deep question, which shows you are thinking.

The two who have answered your query are on the money.

The hypermoderns, that terrible misnomer, because they are no longer modern, belong to the camp who were out to show that Tarrasch was wrong in his discussion on the findings of Steinitz.

In my opinion, having embraced Nimzovich, the arch hypermodernist, is that Nimzovich was right up to a point. But, he was over the top in many ways.

For a beginner, Tarrasch is an excellent guide, as he tended to be of the occupying school. You will learn a lot, as occupation tends to lead to solid positions with fixed aims. But it is not as subtle.  But, you will learn a lot from playing the "occupation" road. 

As you become better, you can go down the "control" road.

But, whatever you do, do not neglect the centre, because if you do, the opponent will find ways to exploit that lack.

Be very reluctant to surrender the centre, as then you have to work from the flanks, and you might choose the wrong flank or find  there is no cohesion in your position, because pieces are not co-ordinated. 

The young modern masters are surprisingly old school in my opinion, as they are rather risk averse, which means dull to many people, which perhaps is not quite fair. 

Oh, I think I see what you mean now, ok.

After writing this, I see that you have ignited a debate between two promising newcomers, which will be worth watching. Good luck. 

Oh, dear, now they have kissed and made up.

Boooring!