Conveniently left out of the cyclist's narrative was the speed differential on sidewalks between cyclists and pedestrians.
Okay, so it's dangerous to the cyclists to be in a high speed/congested road, and it's dangerous to pedestrians for the cyclists to be on the sidewalk. So where are the cyclists supposed to be?
build lanes that are fixed for bicycles. It keeps them off of the road designed for cars, trucks, etc. and the sidewalks for pedestrians. IMO, there should be some type of bicycle roads across the US. I bet it is not that expensive.
It may not be all that expensive if you don't do any planning, engineering, design, research, right of way acquisition, public meetings, stakeholder meetings, clearing, signage, curbing, curb cuts, bike-safe storm grates, lines, traffic lights, lighting, paving, surface treatment, repair and maintenance.
In other estimates (btw, estimates are all over the place, and many articles appear to be running with older estimates), it costs about $25 per sq ft of asphalt. Let's say a bike path is 6 feet wide, to allow for 2 direction travel (this seems kinda tight, but good enough). That's $150 for every foot of asphalt. For one mile, that about $800,000, just for the asphalt. Which ignores everything else I mentioned above.
You could use existing roadway pavement to eliminate new asphalt, although you then incur other costs, many of which are mentioned above.
And then you get differing bicyclist's opinions. Many want protected bike lanes. Do you use flexible bollards or concrete curbing or jersey barriers? Does the line go between the vehicle lanes and the parking lane, or between the parking lane and the sidewalk or curbing? Do you install specialized holding areas at traffic lights?
Bridges are especially costly. How are they handled?
So I'm going to bet with Rothman...I'm not sure what your definition of 'not expensive' is, but chances are, it's not the $ you're thinking.