But why... why do they make their historical signs also highway signs? In the UK we put them on the relevant building, not out on the road.

They're not all highway signs, but if you put them on most buildings in NH, nobody would ever see them. I live in the biggest "city" (which has local, rather than state mandated historical plaques all over it, FWIIW), and it's only 100,000 people.

Blue plaques aren't all that visible from the road when driving, however. To be honest some are hard to spot even on foot from street level.

I guess with the US being a more car-based culture the highway signs made more sense?

Yes. Far more people see them by a road. Also, you can use them for things with no associated building. "In a field near here, Civil War Battle blah blah blah was fought", etc.