There are myriad good and useful things for which there is never enough money. If you want an earful, talk to the maintenance crews sometimes if you encounter them on some remote stretch of the C&O Canal towpath, which at 185 miles is a small fraction of what would be involved in a national bike network. Or talk to the NPS Civil War historians about the issues that arise with highways slashing across Civil War battlefields. Ever been to Antietam? Many have. But have you ever visited the Alfred Poffenberger farm -- not the Julius Poffenberger farm, which is on the standard tour -- or the Hauser house or Hauser's Ridge? If not, you've never seen the confederate left, and you don't understand the field beyond the West Woods. Why not? A highway, and never mind that the NPS owns a lot of ground on the other side of the road. This is an issue on several battlefields.
If Congress ordered it, the NPS would do as it was told, but that would often be a stretch. That's not a knock on the project; it just involves a range of management issues that are outside of the NPS's current organizational structures and skill sets.
There are, however, groups that are working on this, and I suspect the NPS is perfectly happy to cooperate as part of a coalition effort, as long as other partners are willing to tackle the day-to-day management issues. See national bike trail system
I live in D.C. and hang around in Civil War circles. My impression is that the NPS senior management is generally not enthusiastic about small, scattered sites with low visitor rates. These may be very significant sites that should be saved -- there's often no argument about that -- but for the NPS, every independent unit involves staffing, maintenance and oversight responsibilities. We have quite a few small, oddball NPS units in the D.C. area, and cumulatively they aggregate into a big enough complex to justify the administrative overhead. But staffing tiny, remote sites is something the NPS would probably rather leave to state and local parks authorities. For the National Capital Region, see: National Capital Region
Thank you for your very thoughtful post.