I can't speak for Finland, but I think Sweden has a similar culture and the "leave no trace" motto is strong here since nature is considered a communal resource.
I have never seen bins even on major trails here, but I have never seen anything but miniscule amounts of litter either.
If there is no need to pay for the upkeep of bins, why not put those resources to better use like conservation of the park?
How constructive of you.