It is exactly just a convention we agreed on. Once agreed on, everyone uses it and it works. It could have been decided that it should work that addition and subtraction should work first instead of multiplication and division and then everything would have to be rewritten.

One way to sort of get around this is to use something called REVERSE POLISH NOTATION, which places operators and operands explicitly in the order we want to execute them. You place the operands first, and then the operator after them so;

In your first example, to get 7, you would write

2 3 x 1 +

which means take the operand 2 and the operand 3, then apply the multiplication operator them. Now take the result (6) and use that as the new operand and take the operand 1 and apply the addition operator and you get 7

In your second example;
1 2 + 3 x

which means take the operand 1 and operand 2 and apply the addition operator to them, then take the result (3) and the operator 3 and apply the multiplication operator to them which equals 9

So if you want to, you can use that (many calculators actually use that), BUT it is simpler to just memorize PEDMAS (or BEDMAS is you like "brackets" over "parenthesis") and stick to the conventions we always use.

TLDR: Yes, everyone just agreed to use that order.