It's not a bad idea / question for an inexperienced player. You're right that the king is really good at controlling a local area of squares (like the center).
One basic problem is that the type of advantage you gain when your opponent makes a lot of queen moves is very temporary. For example a 2 or 3 move advantage in development can disappear in 2 or 3 moves. A king in the center is typically more costly in terms of moves needed to correct it... and in the process of defending your king if you have to make any concessions in your pawn structure then it will be a permanent disadvantage.
Another problem (and somewhat related to the first) is that in the early middlegame there are lot of pieces on the board, and they tend to compete for squares and lines. A king on e3 blocks the e file and the c1-h6 diagonal for example. So even if there are no real threats to your king (let's say the position is closed) it would tend to get in the way of your other pieces.
One reason pieces like the center is that it's staging them to infiltrate into the opponent's position later. A king doesn't want to do that (at least not until very late in the game). So until then a centralized king will be taking away opportunities from your other pieces.
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Those were somewhat detached logical issues. Maybe more useful are the following two which are more practical:
The first is that when a position starts to open up, and there are some tactics, it's too late to fix something like an unprotected king... you're simply losing. It's not that you need 4 moves but you only have 2, it's usually more like you need 4 moves to fix things and you have zero.
The second is that your strategy relies on your opponent acting in a certain way. In chess a good move is one that you're happy with no matter how the opponent responds. 3 basic reactions to consider are 1.Opponent directly responds to my idea -- 2.Opponent tries to counter with something else and somewhere else on the board -- 3.My opponent completely ignores my move / idea.
So you might ask "if it didn't bait my opponent's queen or any other piece, would I still like it?" Maybe your answer is "it would support my center" which again is not a bad idea for a new player to have, but experience will show you that inevitably some files / diagonals will open, the king will be a liability when attacked, and a liability for its blocking friendly pieces from moving around.
This is almost certainly a very stupid question to ask but I still want to know, does the king have potential for baiting out pieces like the queen? The king's moveset is actually quite useful for controlling the center, so if you can use him to bait, say, a queen into a vulnerable position, then you can punish pretty hard, whether by gaining a positional advantage or a raw material advantage. If you play your cards (or pieces) right, you can still keep the king protected.
Again, this is stupid and im not that good at chess but I find it to be an interesting thought.