Why would it be incorrect to balance the equation by changing naoh to na2oh2 instead of 2naoh

Beacuse Na2OH 2 is completely different compound than 2NaOH.

By NaOH we mean two molecules with one sodium, one hydrogen and one oxygen atom each.

But by Na2OH2 it'll be understood that 2 atoms of sodium one aton of oxygen and 2 arom of hydrogen was used ro make up this one molecule.

Here's a simple example,

You have
H2+ O2 > H2O

while balancing,

you're supposed to write H2O as 2H2O
which means 2 molecules of water.

And when you write it as H2O2 insted it means that you are forming and oxidizing and reducing agent, which is a waste (toxic waste) for our body and can kill us, which means it has the opposite property of water.

And this is the reason why you should balance it by placing the numbers on the far left side than subsripting it below atom of different elements so that you can make the same compund everytime.