Noted that you didn’t answer my question - the answer is I have 14 litres of milk. 2+3+3+3+3=14 litres. When you did “arbitrary addition first”, you got 20, which is wrong, which is why no other order of operations rules work than the ones we have.

You can’t change how equations work and then expect all equations to work the same after the change

In actual fact the point is that they will except for what ever your new notation is. e.g. if we instead defined + to mean multiply, and x to mean add, then we would do + before x, and again, that would be the only order of operations which works. i.e. the only order which gives us 14 litres.

that doesn’t mean there is anything fundamentally wrong with having a different system of writing equations in which operations are executed in a different order

No, and if you did that, you would again arrive at only one order of operations rules which works, cos I still have 14 litres, and the Maths in this new system still has to give an answer of 14 litres, not 20.

Our whole system of writing equations is just a convention

Nope, it’s all rules, found in any Maths textbook, and if you don’t obey the rules you get wrong answers (like you did when you got 20).

But there is no fundamental truth behind it

Yes there is - I have 14 litres, and only 1 set of order of operations rules gives that answer.

only that it is simpler for the majority of use cases

If you follow the rules of Maths then it is correct for every use case. That’s why they exist in the first place.