I agree, I think it's better suited to .org.uk than .co.uk. Not sure there would be much demand from actual libraries though. I reckon most local libraries maintained by councils would just have a subsection of the council's website, likewise university ones. Any private or niche library e.g. the London Library would most likely want its full name as its domain. Would be ideal as a brand for an online library project though, perhaps ebook only.