Maybe your chains get gunkier than mine. I find that just wiping the chains off with a shop rag keeps them clean enough for me. My issue with soaking them in mineral spirits is that you are cleaning out all the lube from places that likely is not very contaminated and possibly moving grit into their place. As well when you do let the chain dry out you will have to hope that the lube gets down into all those places that it was removed from before any damage to the wear surfaces can be done after you use the chain again. Or if you lube the chain while the wear surfaces are still wet with mineral spirits then perhaps the mineral spirits will not be displaced by the lube.
You can leave the container of used mineral spirits open so it can evaporate and leave you with just the solids and other stuff that won't evaporate. However I don't know if that is completely hunky dory by the EPA. And of course whatever is left is probably more a hazardous waste issue but maybe below the amounts that EPA and others are concerned with for disposal.
So if concerns for the environment are primary for you then just wiping off the chain would seem more reasonable. Is the mineral spirits really about extending the life of your chain, which I doubt it does. Or is it more about easily making it cosmetically pretty?