Sure enough, botanical gardens do grow, for instance, Coffea arabica in hothouses, and, according to Wikipedia, its growth conditions do not seem impossible to achieve in a European or Northern American backyard:
C. arabica [...] does best with 1.0–1.5 meters (about 40–59 inches) of rain, evenly distributed throughout the year.[...] The plant can tolerate low temperatures, but not frost, and does best when the temperature hovers around 20 °C (68 °F). [...] C. arabica prefers to be grown in light shade.
I have never heard of people having them in their garden and actually harvesting coffee beans. It does make sense to me that it may not be economical to have commecial plantations in Hamburg or Berlin, but say I had a little waste heat and a glass house I could divert that to, are there any requirements that I can't fulfill in the moderate latitudes?
In fact, to me, the above description sounds like you could easily have those trees in lobbies and canteens indoors.