Yes that is their problem, the strategic route they had before doesn't work any more so they need a new one. When they planned it I think they assumed they could build the now aborted Swainswick - Batheaston bypass to avoid Bath.
Others have posted while I was writing this - I have decided still to post as it backs them up and has a few extrasIndeed - you have the very curious Batheaston bypass (connecting the A4 East - West and the A46 headed north) crossing the River Avon twice that at one point on the same side of the Avon as the road headed south (A36) and only about a quarter of a mile from it.

The way around it shown on this map is via the Clevedon Bridge which - however - is a revered piece of history and accessed along roads like the London Road and Bathwick Street which are unsuitable for HGVs, or for an easy increase in vehicle numbers. Other ways are the toll bridge at Bathmapton (and I'm sure there are weight limits there) and through the old town and across the old bridge at Bradford-on-Avon with problems with air quality, congestion, vibration and so on, and which has a weight limit which is very visibly applied.
There is no blindingly obvious route north to the M4 from Warminster. There is a strong case for a road (the new A350) that allows traffic to bypass Westbury, from the A36 where it crosses the main railway to the West Country, parallel to the railway to the Industrial area north of Westbury station. That industrial area is altready linked to the M4 via the A350 though there are pinch points at Yarnbrook and in Melksham north of the Farmer's runabout that already - err - need attention.
We shouldn't be looking at the strategic route in isolation either. Resident population growth is set to be and mandate to continue to be explosive, but the commercial / economic hub for that growth is the Bath and Bristol area, and good mass transit links are needed - beyond what we have at the moment, as the private car infrastructure already creaks at the seams.