This isn’t about limits of accuracy

According to who?

According to me, talking about the origin of the 0.999... issue of the original comment, the "conversion of fractions to decimals", or using basic arithmetic to manipulate values into repeating decimals. This has been my position the entire time. If this was about the limits of accuracy, then it would be impossible to solve the 0.999... = 1 issue. Yet it is possible, our accuracy isn't limited in this fashion.

You still haven't shown why you're limiting yourself to basic arithmetic.

Because that's where the entire 0.999... = 1 originates. You'll never even see 0.999... without using basic addition on each digit individually, especially if you use fractions the entire time. Thus 0.999... is an artifact of basic arithmetic, a flaw of that system.

Different systems for different applications.

Then you agree that not every system is applicable everywhere! Even if you use that system perfectly, you'll still end up with the wrong answer! Thus the issue isn't someone using the system incorrectly, it's a limitation of the system that they used. The correct response to this isn't throwing heaps of other systems at the person, it's communicating the limit of that system.

If someone is trying to hammer a screw, chastising them for their swinging technique then using your personal impact wrench in front of them isn't going to help. They're just going to hit you with the hammer, and continue using the tools they have. Explaining that a hammer can't do the twisting motion needed for screws, then handing them a screwdriver will get you both much farther.

Limits of accuracy isn't algebra.

It never was, and neither is the problem we've been discussing. You can talk about glue, staples, clamps, rivets, and bolts as much as you like, people with hammers are still going to hit screws.