Nope. I know the stresses are not great in that area, but that pitting is a great source for stress risers. Significantly increases the chances of cracking and breaking. I personally would not risk it.
That's exactly what I was wondering about when I posted this.
Grind them out then.
Sorry, but we are starting down a path that could very well make this worse for the OP. It appeared to me, and not if addressed already, seems like the spindle has already had some mechanical surface de rust prep in posted pic. That was smart, and only improved matters. Going further with grind marks, causing minor localized heating, and/or grind marks orientation, etc, are a risk, and not worth it. Additionally any metal removal is hard to see as a plus. If there was one or two serious depressions, which I don't see, there would be the issue of concentrated stress riser. The fact that there are numerous rust cavities, actually spreads the stress out over a larger surface area, minimizing any single large stress concentration. As also already mentioned, I always coat the area shown pitted with grease, for this very reason, due, to exposure some how, by immersion, or condensation.
