Why would you need floating point arithmetic for anything? You can do all mathematical operations with fixed point just as well.
And using relative coordinates everywhere might not be practical either. I don't understand why you are defending using floating point for everything so hard? There are cases in which it is not a good choice.
Why would you need floating point arithmetic for anything?
So let's say you have your 128-bit integer coordinates and now you want to do something useful with them. Like interpret them as a 3D vector and multiply by a typical transformation matrix.
Now you have all these intermediate terms inside the matrix gaining and losing precision. Rotation elements are going to have a range of -1 to 1. Translation elements have a similar range as your input coordinate system. Scaling elements have an almost arbitrary range.
You can't use a general purpose matrix library any more. You have to track down every little multiplication and addition and analyze it for precision loss. Many will need to be converted to least fixed point numbers.
You can do all mathematical operations with fixed point just as well.
Some things are much much better, some things are much much worse.
For something like rotation, you're multiplying by -1.0 to 1.0. You might use 64.64 fixed point numbers for this, but then you've wasted half the bits of precision you paid for.
Floating-point certainly has a lot of potential for surprising behavior. But it usually allows you to get reasonable accuracy from a naive combination of basic operations.
And using relative coordinates everywhere might not be practical either. I don't understand why you are defending using floating point for everything so hard? There are cases in which it is not a good choice.