So do we know the axle thread dimension? 3/8"x24TPI or 10x1mmpt?

The axle issue shown is not what the industry sees as an issue. It shows thread form damage which is usually from bad securing, loose nuts or cones, axle rotation within the drop out. Question- Which side of the axle are the damaged threads on? The drive side or the brake reaction arm side?

Coaster brake axles don't bend usually barring axle peg use. Their outer bearing are fairly symmetrically positioned so that the forces on the axle are fairly even WRT each side. This is vastly different on a freewheel hub (hence the cassette design which has more evenly located bearings). Over the years the industry has found is it design (bearing placement/load balancing and axle diameter) that makes the bigger difference WRT bending (compared to axle material strength).

So my second question, which I sort of asked in post 5, is whether a higher strength steel bolt/axle will have greater thread deformation resistance and is any increase of this enough to prevent the damage shown. Andy