The difference when you get the infinite number of 9s on the 0.9999999… is 0.0000000…0001.

No, it can't be. If you know where to put that last "1" then you don't have an infinite number of digits anymore. That is the difference between the infinite and finite number of digits.

1.00000000… is vastly superior to 0.99999999… as a way of representing 1.

Is it? That's an opinion. When you're talking math, you're not really dealing with opinions. Therefore, as I said to tsuwm above, it may be ugly to use 0.999999..., but that doesn't make it untrue.