I bet it's because builders are on a budget that they stick to the traditional standard tiles/cement/asbestos combination at the gables. Now plastic is popular because it's labour saving. I often use blue slates instead of asbestos, overlapped and then fill the gap between slate and tile with cement.

WBP has a limited lifespan in wet conditions, it will rot, the glue that bonds it together is waterproof, the core is not, so unless you can paint and maintain every side and edge of it, you will be doomed! I think it would be a really bad idea to use it as undercloaking.
Is condensation an issue outside the building?

Are the plastic eaves protectors you refer to, those black plastic L sections approx 300mm wide? I do think they are reassuring because some roofing felts rot at the edges where it drapes into the gutter and water that has found it's way under the tiles can end up running onto the top edge of the fascia and down the back of it. I often find myself retro fitting 300mm black plastic dpc by sliding it under the damaged felt, when damage to the original felt has occured.

Blue slate = natural welsh slate, it can be bought as thin as asbestos and is often recycled. Is the timber frame on the external leaf of the construction? The undercloaking usually only comes into the external leaf, if that's masonary then there shouldn't be an issue. You could insulate between a slate or cement board undercloak with something thin, or protect the timber frame wit more dpc.

I have a vague feeling I've seen them used on agricultural buildings in East Yorkshire? Aren't they a bit bulky looking? Where tiles meet the verge, usually every other one is a 1 1/2 width tile to allow for the bonding pattern, are these verge tiles in that format? How is the lap allowed for?

Hi Julian, I have renewed several verges because of rotten battens 'protected' by wet verges. The problem with a wet [cement] verge is that it is porous and therefore directs moisture just where you don't want it- into the end grain of battens. Cement also expands and contracts with moisture as well as temperature fluctuations so often cracks exacerbating the problem.

I don't like the look of plastic cloaks but they do resolve these problems

Tried using clay plain tiles as the undercloak under profiled roof tiles? Mortar-bedded face-down (i.e. any dishing upward) on top of the outer skin and hanging outward 2", batten ends resting on top as far as the outer skin face.
I hate cloaked tiles - they sort of blur the crisp shadow line at the verge. Especially the cloaked concrete tiles.
How about the traditional timber detail that has a 1" thick verge fascia, its top edge rising up past the edge of the tiles, with a 6" wide capping board fixed to the fascia's top edge, which covers the edge of the tiling by 4" and overhangs the fascia by 1"?