On the economic side, are bikes registered and bike owners paying for tabs each year likes cars in NYC? It would seem that would go a long way towards paying for new bike lanes over parking.
There exist a couple of studies that show the costs of administration of a bicycle registration program is more than the revenue collected when you make the registration cost reasonable. (Sorry, haven't got links right now.) That's before you get into defining exactly which bicycles have to be registered, and figuring out how to enforce it.
If we are going to put in more bicycle lanes with the bike owners having ownership and not just taking space from the already taxed car drivers, money needs to be collected. The US needs to start actually paying for things. Roads for vehicles (trucks) are at least used for delivery of everyone's goods, bike lanes and trails don't have that secondary use. Car parking removed for bike lanes can be a profit center.
I don't understand the "which" part. Wouldn't it be all bikes that are legal on the bike paths? That's how motorcycles work for roads.
Bikes damage the road orders of magnitude less than cars. Without having run the numbers, I'd wager that the city could actually save some money in the long run if more bike lanes would decrease car traffic.
It still costs money to put in the lanes. They may last longer, but there is a startup cost. I doubt there is a study that shows more bike lanes would decrease the actual amount of traffic to make a material difference in road maintenance costs.