It may well have been a good idea at the time if the main purpose of the route was for long distance traffic from London to Exeter but since then things have changed.
Er are you sure? the route is even moreso a direct route for long distance traffic from London to Exeter today than it was in 1809?
Upgrades have been done piecemeal to provide relief for the towns and villages on the route rather than with the intention of creating a second high quality route from London to Exeter.
The upgrades were done piecemeal but as part of an overall strategy to create a high quality route from London to Exeter. The first bits to be done were narrow river crossings such as Petherton Bridge (which were wide S1 (look at the Yarty bridge west of Chard on the A30 and you will get the idea), then the towns and villages as these were the main congestion points for long distance holiday traffic, by the '80s the gaps were busily being filled and plans existed to complete the route. Most of the upgrades that were done could never have been justified by local traffic levels which spike on summer Saturdays but only as a strategic route under then then predict and provide policy.
The fact that the road passes close to Stonehenge and through the Blackdown Hills will likely prevent the route from becoming this high quality route.
The Blackdown upgrade was ready to go in the late '80s, having passed all enquiries with barely a bleat, when the government ran out of money and cancelled it just before construction (the cancellation causing much local outrage). Only one thing proved contentious at the enquiry, the plan to have a roundabout rather than grade separated junction at the A30/A303 junction. (which was presumably the idea of the "Black Cat" roundabout propagation society
If the A30 was upgraded instead, there is of course a handy canyon 50m wide all the way from Chard to Honiton that goes right through the Blackdowns that it could use. For some reason, the people who built the original Chard to A303 turnpike through the Blackdowns forgot to use it and carved a spectacularly engineered route through the Blackdowns instead
As for Stonehenge, it could fairly simply be bypassed by a route running north of Bulford Camp and Larkhall, then dropping east of Shrewton to rejoin the A303 west of Winterbourne Stoke. A significant amount of the land needed is already government owned (shown on maps by the numerous Danger Area endorsements).
If the A30 had been upgraded instead there would not have been the difficulty with Stonehenge
...but there would have been a bigger problem at Salisbury. I recall the A36 bypass of Salisbury was cancelled due to general outrage.
and the road would also have provided relief for places like Salisbury and Yeovil which are larger than most of the places bypassed by the A303.
The A303 is
the Salisbury and Yeovil Bypass.
The A30 was detrunked and the A303 trunked after the authorities concluded as early as the 1950s that upgrading the A30 was not feasible. If it could not be done then, it is even moreso the case now.