When was the last time houses were demolished in a city for building more roads? We should treat space for traffic infrastructure as a fixed supply and take away space from cars for building cycling infrastructure. Building paths along rivers or through parks or such is almost always completely useless for commuters. Existing roads define the efficient connections between places people want to go. If you want cycling infrastructure that people use, you either need to put it where the roads are, or demolish housing to build new efficient routes.