I guess it is reasonable to run some experiments, set up some bike lanes for a period of time. If they are used, keep them, if not maybe consider removing them.
Good point regarding the costs. The other advantage of dedicated / purpose-built bike paths is they likely don't have to be built to the same spec as ones designed for vehicle use (I assume - not a civil engineer).
Careful, this often ends up with cities and towns building isolated pilot bike lanes that go nowhere and then ripping them out when nobody uses them.
The value of a bike lane isn't in the lane in isolation, in the same way that the value of a street isn't in that street alone. It's in the ability of that lane/street to get you where you need or want to go.