> To expand, I think the main reason the Swiss method works is because the country is relatively small

I don't think that's relevant, as there are many small countries with the same problems as the UK and the UK is only medium-sized.

> and well-aligned.

That's the crux of the issue and it's not because of population size. Small countries are no more aligned than large ones (or medium size like the UK) in general.

Why is Switzerland more aligned politically than its peers? Why is social cohesion higher?