The BBC does make a motoring programme in the style you describe, I’ve mentioned it before and they even featured a Morgan or two.
Available on the BBC iplayer, go to channel Alba, Air an Rathad.
The downside is, it’s Gaelic with subtitles and done on a tiny budget, but they did managed to scrounge some nice cars.
Ewn thanks for the tip. Today (being a bloke with too much time on his hands) I watched a couple of episodes of Le Anne's trip around the North Coast 500 in the ersatz beetle. At first I thought, nah, it's a Scottish Tourism promotion - however it does have appeal. The eclectic music choice, the landscape, the chats with the locals... It was also appealing because a few of us Mog owners here in the land-locked centre of Europe are in the early stages of planning such a trip. And I have great memories of working with a BBC Alba film crew who were great company but refused to go to bed at a respectable hour

but that's another story.
So in that program brief I was beginning to write last night there would be elements of Air an Rathad but also The Trip (Coogan and Brydon) only the trip would centre on a Morgan and a grumpy curmudgeon (ok it could be a pre-war Riley or Alvis or anything of real character) who is steeped in motoring and cultural history and who keeps stumbling upon places that inspire dialogue and reflection e.g. old race tracks, the place where a great driver met his end, a crumbling car factory etc. At the same time he would have to keep calling home to explain to his missus what he's doing and why and his family just wouldn't understand and we would all wonder if in the end our hero was unfit for the modern world and would just keep driving until he ran out of road and then...
But as Clipper intimated, it would not be a Top Gear type hit except among TM'ers and other anoraks. But just maybe, with the right driver/narrator and the right script and car, like The Trip, it could win an audience for at least a couple of episodes. SlÀinte.