[exmadscientist]

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!)