Juzt a small note:
It's free only for citizens of Tallinn, not for e.g. tourists.
I wonder if that was a rational decision. Is the cost of authenticating higher or lower than the revenue gained from tourists? If the revenue difference is actually that large, they probably could have just rolled it into the typical "hotel taxes" most places have.
The revenue gained is not from tourists but from people living in neighboring municipalities (but working in Tallinn) registering them as citizen of Tallinn and therefore bringing their tax money.
Impressive. Redstone Arsenal in Alabama only has 40K people or so. At least in the 90s when I was at the Ordnance school. Which has apparently moved to Ft Lee since then. The free buses were rather convenient.