Mineral oil is a petroleum distillate and does not cure. In order for oils to dry, they have to have drying agents added to their composition. Boiled Linseed oil will dry, because it has metallic driers added to it (it isn't really "boiled" anymore). Otherwise, pure linseed oil would never fully cure either. I only use mineral oil on items that come into contact with food, such as cutting boards.
Some folks have reported good results using mineral oil as a finish. If mineral oil works for someone, I won't argue against them using it in their specific application, but I would suggest that this is not a good practice for all applications. Mineral oil may cause problems if one tries to top coat it with another film finish. As you have discovered, it can leach out of the pores of the wood for a long time after it is applied. Mineral oil was never designed to be a wood finish. It's primary use is as a natural laxative. The fact that it can work on wood, in some cases, is probably more a matter of a fortunate convergence of circumstances than anything else. I would recommend if you want to use an oil to pop the grain, that you use something specifically intended to for this purpose, such as boiled linseed oil. But even BLO isn't really a finish, per se. It requires a top coat of some kind to really offer any kind of protection or anything other than a dull sheen. If you want a protective finish, then use a product designed for that purpose. You have many good choices.
