I've never understood the fan folding idea for long yardage. I pre-wash up to 10 yard cuts as I described above (gentle cycle, etc) and they come out wrinkle free, ravel free, chemical free, bleed free, grain restraightened, and evenly shrunken. Those last four are the reasons I pre-wash, the first two are bonus points.
It would seem to me that fan folding for the wash would possibly (likely, imo) result in:
a) damage to the fabric - heavy, wet fabric under agitation pulling on pin holes that most likely broke threads when they were first inserted because the pins are usually larger than the spaces between fabric fibers and were forced through multiple layers at the same time, definitely in batiks
b) uneven shrinkage - fabric with limited mobility would potentially shrink unevenly and result in warping
c) misaligned grain - locking the fabric in place prevents any straightening of the fibers necessary to realign the grain; it also potentially distorts the grain even more than before washing
d) all of the above
None of these problems is blatently visible if you aren't looking for them, but that doesn't mean they aren't happening and making a difference to your sewing accuracy. Just some things to consider.