I've seen many times how some people react to a single bus lane or even a tiny bicycle lane as though cars are getting the raw end of the deal when 90%+ of infrastructure is for cars.
I am all for it out of general principle, but most car drivers will likely disagree.
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).
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.
And, more abstractly, if a dedicated bike lane means more people taking the bicycle, that also means fewer cars on the road, making it that much more pleasant for those who continue to drive.
Speaking as someone who enjoys driving, I'm all for dedicated bike lanes, even if that means reducing car lanes.
We’re so instinctively competitive though it feels hopeless.