I think a lot of these answers are losing the forest for the trees.

What are the two most pointless symbols in mathematics education?

The symbols for multiplication (×) and division (÷).

Why? Because they disappear when you get to algebra.

Multiplication instead becomes the default of two values are next to each other without an operator, then they are multiplied:

Instead of 5 × x, we just write 5x.

All division turns into fractions.

Now think about something like a polynomial. For example,

5x^2 + 4x + 3 = 0

Is much easier to write than

5 × x^2 + 4 × x + 3 = 0

Which is also easier to write than

5 × (x^2 ) + 4 × x + 3 = 0

Now consider how the order of operations makes expressing the terms of a polynomial straightforward:

exponent first, so the variable can be raised to the appropriate power given for each term.

Multiplication next, so each term can be multiplied by a constant.

Addition last, for the final combination of fully calculated terms.

PEMDAS makes writing a polynomial straightforward and helps the notation capture meaning.

Obviously, there is more to math than polynomials and as other answers have touched on, there are lots of reasons why multiplication comes before addition.

I would also like to add that subtraction doesn't exist and it would be better if we stopped teaching it once negative numbers are introduced, but I do think that ship might have sailed.