My experience is based on using 22mm and 13mm LVW in an XLT C8 with and without the 0.63 reducer/corrector.
I found a distinct improvement in the middle third of the field. The central third was pretty sharp either way.
Based on what i had read at the time I assumed that the the improvements were due to the decrease in focal curvature. However CNer Frank ( frankstar8..i think) described the theory behind the improvement that it corrects for coma and not focal curvature per se. So while the aberrations are indeed reduced, it was not a "flatter" field per se..which would have require a decrease in FC. Rather, the improvements are due to a decrease in coma.
I believe this is also what Vla is stating.
Well, yes, it does reduce coma a little but it also flattens. And by that, I mean, without it, you find stars in focus at the center but out of focus at the field edge. With the r/c in place this is nearly eliminated. And this is what I and others refer to when we say it "flattens" the field.
If you care to look, there are threads here where this has been debated over and over. Some argue that it can't do that and they base their argument on optical theory and such. But there are legions of users who from actual visual experience will attest to that fact that it does indeed flatten the field (by my definition above)