we redo shells all the ...
we redo shells all the time and you cannot get the black, out of the white shells they are embetted,
we paint them and they look great if you use a good color to paint them.

I should think
that once the glass fibers are exposed -- ie, no longer encapsulated in the resin -- they would serve as conduits to liquid-borne soils. Sanding the shell would almost immediately lead to this condition, I think. The glass fibers were never intended to be uncovered. Of course, weathering and/or extended wear might also lead to this condition.

The origin of these black colored
fibres is quite simple. Glass fibres do not connect with the polyester resin, so they are coated with materials that connect both to the glass and to the resin without affecting the polymerisation of the resin. Unfortunately these coatings are water soluble and through capillarity they will be replaced by mostly organic material that is present in the water. Hence the importance of gel-coat to protect the part of the fibre reinforced polyester that holds the fibre. The gel-coat has not the mechanical strength so it has to be combined with fibre filled material. There is simply nothing you can do, other than being careful with them because they have lost significant strength due to the fact that there is no link between the glass and the polyester.
In sailboats this penetration of water is often referred to as glass fibre cancer. A small crack that is not immediately protected will quite quickly develop to a large patch.

we have found that painti...
we have found that painting them and using a nice semi gloss clear sealer makes them look really nice,
unfourntaly you will not see the old fibers, that the original chairs are most famous for, but none the less they look nice and clean

if thats the case don't ...
if thats the case don't bother to waste your time leave them alone .
I do so many shells in our business and they all come in looking like shit!! at least if you put a new fabric or vinyl they have a chance to look good in your midcentury modern home, if you leave them with the 40 year old look why bother i would not want any old cracking vinyl with crappy marks on my chairs in my home, We try to clean the fiberglass for the customers before we ship them back and most of the time they really dont get the marks off we use paint thinner and it cleans them up some and they look better.

Claus
As already discussed once the gel-coat is gone you've got issues of more soil creeping into the fibers, as well as the fibers creeping into your skin. I had an old drilled out chair that I took to an auto-body shop and had them spray a clearcoat on. The result was much better than painting.

A solid coat of paint makes the surface appear dead and lifeless. The clear-coat preserved the organic quality of the fiberglas, even if it didnt quite match up with the original gelcoat. (The gelcoat is more integrated into the fiberglas, whereas the clear-coat definitely 'sits' on the surface. However, clearcoating is the closest thing I've found to the original finish)

Also - like you've mentioned, it preserves the history of the chair - which is why we like them right? If not preserving the history you may as well get one of the new polyprop Eames chairs.