You have a point. I tend to dislike arguments about mathematics that start with "well, this definition is just a choice" because they don't capture any substance about any actual math. As a result, I tried to head that off by (perhaps poorly) making a case for why this definition is a reasonable choice.

In any case, I misunderstood the nature of what you were saying about the convention, so I don't think we're in any actual disagreement.

I might also turn that argument back on you and repeat what I said before: "if you meant 2, why not just say 2?"

If I meant 2, I would say 2. However, our system of writing repeating decimals also allows us to (redundantly) write the repeating decimal 1.999... which is equivalent to 2. It's not a very useful repeating decimal, but it sometimes comes out as a result of an algorithm: e.g. when you multiply 2/9 = 0.222... by 9, you will get 1.999... as you calculate it, instead of getting 2 straight off the bat.