Gonzalo, let me rewind to your opening post, which for reminders said this:
I'd like to make a good selection of papers so I bought a few test packs and downloaded the Bill Atkinson test image. I was about to start printing when I thought whether I should soft proof the image for each paper or not. If I soft proof, I'll have better results and see the properties of the paper but it won't be the same image for all the different papers so it might not be a good comparison. On the other hand, if I just print it without prior soft proofing to see how the paper renders the image, I'll be able to see the differences among the papers but they might not be showing their full potencial, so the comparison isn't good either.
In the final analysis, it all depends on what your objective is. Perhaps we haven't focused enough on that. If your focus is mainly to see what each paper produces using a standard test image with no manipulation, the soft-proofing is indeed irrelevant. The printer/paper/profile will do what they do and you compare results. That certainly gives you indicative comparisons, but it may not give you all you want to know about full potential from a real-world photographic print workflow, because the photos will all need editing (a test target does not) and the kind of editing you do would likely vary depending on the paper/profile being used.
So, if your objective is to see how you can optimize the print for each paper, then I wouldn't recommend using that target in the first place. As there are so many kinds of images, there is no "one size fits all". So in this case you would select a number of photographs having the characteristics that are most relevant to you, and print the same photo using no more than two or three different papers, each custom-optimized with soft-proofing to see which gives you the most pleasing outcomes. In a way, I did just this in my review of the Epson Legacy papers, so if you go there, you will see how editing plays differently for different papers/profiles and different kinds of photographs - and where soft-proofing is so useful. Once you have a small pile of prints of say at least half a dozen different kind of photographs each printed optimally on several papers, you will gain an appreciation of what paper you like best for which kind of photograph.