I didn't know the junction with the A618 had been a staggered crossroads. I have always wondered why the two routes didn't meet at a roundabout; it would have meant a simple realignment of the A618, half of which was done anyway.
No idea for sure, but my guess would be that it was due to the difference in levels since the old alignment was on a gradient where it meets the bypass, so would have had to be raised/lowered either side of the A57 to tie into a roundabout anyway.
The old staggered crossroads were very dangerous - the number of KSIs at the eastern junction was very high. However, as mentioned in another thread, I think there was a funding problem here - as the A57 was a trunk road as far as the roundabout to the west, from where Rotherham MBC (briefly) and Sheffield CC are the highway authorities into Sheffield city centre. Clearly the road has a local function at this point, so I suppose it would have been difficult to get an improvement scheme into the TPI.
BTW, hope you don't mind my changes - just a few additions!