How bad do spots of surface rust have to be, to threaten the integrity of a steel frame?

I have a vintage frame (SLX) with a few 1/4" wide spots of surface rust where the paint is chipped. But radiating out from some of these spots are squiggly black tracks which seem to be under the paint, and won't come off with Goof Off. I suspect those are rust tracks.

My plan has been to sand the rusty spots and touch up the paint, while leaving the black tracks alone. The bike will then be placed into duty as a high school boy's school bike including being locked up in the rain. I imagine any rust under the paint will continue to develop.

Will those rust tracks ever compromise the frame? If left untreated, would the spots of surface rust ever do so?

I'm basically wondering if we treat rusty chips simply for cosmetic reasons, or if there are functional reasons to do so?