Not so much for polling data, but some governments do allow access to coarse election data.
Australia's was enough that the unfortunately complicated math of their election system was repeatable and verifiable (Can't find the post about it, however)
Good point. However, in my experience messing around with choropleth maps, I often find myself resorting to web scraping in the end when I want something more current (opinion polling). Despite this data being seemingly everywhere, and companies often wanting you to use it (with attribution) so they can get advertising for other services, they never seem to have an API.
Australia's was enough that the unfortunately complicated math of their election system was repeatable and verifiable (Can't find the post about it, however)