stairs coming apart

I've got a set of basement stairs that i did not build. original to the house, about 24-ish years ago. the treads are comming loose from the stringers one by one. its regular softwood stringers with hardwood treads and they used really thin gauge nails to put them down. like pin nails or trim nails from an air nailer or something, they look more like wire than nails. ive never seen it before.

my plan is to take them all up, drill pilot holes in the treads, 2 holes for each stringer for a total of 6 holes in each tread. then counter sink and use screws and construction adhesive to put them down permanently.

does anyone see a problem with that plan?