Betjeman fell in love with Cornwall as a child and visited at least yearly until his death. As you say, the road links London and Cornwall: he spent a lot of his life on it.
The geography of Devon and Cornwall dictates transport routes: with coasts to north, south and west, the A30 is the main route in and out. When you live in such a place the main connector is something you develop quite a visceral love/hate relationship with. This is more pronounced before roads are upgraded to dual carriageway and motorway.
I live in the Highlands and can attest to this kind of relationship with the A9, it both connects us and divides us from the rest of the country, it is a character in our story. For the A9 this can be seen reflected in the role it plays in works by those who rely on it, Michel Faber in Under The Skin, Ian Rankin in Standing in Another Man’s Grave, Christopher Brookmyre in Boiling a Frog and in Black Widow.... and so I suspect it is with Betjeman and the A30, it is the road he knows like the back of his hand.
Interestingly he presumably wrote about it at least in passing before he meditated on it poetically.
The Shell Guides were developed by Betjeman and Jack Beddington, a friend who was publicity manager with Shell-Mex Ltd, to guide Britain's growing number of motorists around the counties of Britain and their historical sites. They were published by the Architectural Press and financed by Shell. By the start of World War II 13 had been published, of which Cornwall (1934) and Devon (1936) were written by Betjeman.