Question

Why was the BODMAS theory accepted by all?

Answer 1

The reason for the order of operations is that sums of products come up more often than products of sums, so we want an order of operations that lets us write sums of products efficiently.

Here is a sum of products:
$x.x+2.x.y+y.y$
$x.x+2.x.y+y.y$

We can also write this polynomial as a product of sums:
$(x+y).(x+y)$
$(x+y).(x+y)$

Here's another sum of products:
$x.x+x.y+2.y$
$x.x+x.y+2.y$

However, there's no way to write it as a product of sums. This polynomial cannot be factored.
No matter the sequence of addition and multiplication, we can always distribute to write the result as a sum of products. That's what you'd do if you wanted to check whether
$x(y-1)-(y+49)$
$x(y-1)-(y+49)$ is equal to
$(x-1)(y-1)-50$
$(x-1)(y-1)-50$, for example.
Mathematical notation was developed by humans over centuries. When people got tired of writing, "From the product of the first unknown and one less than the second unknown, subtract the sum of the second unknown and forty-nine," they gradually started developing more and more shorthand that eventually turned into modern mathematical notation.

As usual for shorthand, people tend to make more abbreviations for things they use a lot. That's why we use lol for "laughing out loud" but not for "Can you buy chicken on the way home?" though you might say "can you buy chicken plz," because "on the way" and "please" are common uses.

For the reasons above, people found themselves arranging functions as sums of products a lot well before modern mathematical notation and order of operations, and so as people developed a shorthand, it assumed that folks would want to group products together by default and add later. If a different grouping was intended, the author would have to clarify.