Back in the day when I used a proper paint stripper it would actually raise the grain of the wood and then it had to be knocked down again. I prefer a stripper that gets it mostly done with out raising the grain, then I can lightly sand and repaint. If you want to re-stain then yeah you really need to get down to the bare wood.

I find that strippers on heels are a very expensive way to get paint stripped off anything, but it is more fun to watch tho