Those fields are part of a UNESCO world heritage site, where countless neolithic artefacts (including human remains) would be disturbed or destroyed by construction.

Besides that, the road is very busy and noisy, and is a huge blight on the site itself. Visitors will get a much better sense of how Stonehenge felt for ancient visitors without the stinking, roaring A-road right next to it!

It is a very sensitive area for conservationists and historians. Pretty well guarantee that if they started to dig a hole to build a new road they would find something of interest that would delay the build and make the cost sky rocket.