Why? (To be clear, I don't disagree, but I also think it's important to back up assertions like this.) There are possibly better middle ground algorithms ("superblock accumulation", "tree sum", etc), which are both more accurate than naive reduce and faster (because they allow vectorization), but are less accurate than compensated summation.
It's absolutely possible; there are a few options for how to actually do it. It requires either multiple passes or sorting or accumulator memory proportional to the exponent range of the type (hundreds of bytes for double). Any of these are significantly slower than other accumulation options, but some of them only by a constant factor. "Kulish Accumulator" is a pretty good search term if you want to learn more about the subject.