A really interesting review. The idea of relative error makes sense in most cases, but when we need to do subtraction and difference matters, maybe absolute error is actually better.
If you are doing only additive operations, then, yes, absolute error might actually be the best choice. But as soon as multiplications start to show up, they are enough trouble that they tend to dominate the whole error propagation show. Since many real calculations have multiplication in them, you end up having to optimize the whole thing for multiplicative operations, and so we end up just using relative errors everywhere.
You can, of course, do a very specialized optimization for one particular algorithm, but that tends to not be a very good use of time. Usually. (Counterexample: Kahan summation!)
Subtraction is the very case where relative error might matter most, and error relative to magnitude of the original unsubtracted numbers causes the most surprises.
Absolute error has useful applications, without any doubt, and regardless of arithmetic operation, but it probably doesn’t make sense to say it’s “better” without a specific problem in front of us, and without specific goals and priorities. Error tolerance is always up to the user.
You can, of course, do a very specialized optimization for one particular algorithm, but that tends to not be a very good use of time. Usually. (Counterexample: Kahan summation!)