In the UK at least, researchers have many options for research fellowships of 3-5 years, paid, many with total academic freedom to do whatever you like
My partner just got accepted to one after spending 3 months applying to 5 fellowships — an 8% ratio of application:research time.
In an Oxford or Cambridge college, you're working, eating and (for younger fellows) living in college with many other smart people. Sounds like a lot of cross-pollination of ideas happens there.