You are right that money is XOR. But cycling takes people of roads and improves the overall system while being very cheap. Also, you don't need dedicated super dutch style infrastructure to encurrage cycling. Making it safe for walking and cars to interact, ALSO makes it much, much better for cycling. Its a mistake in thinking that 'cycling' infrastructure is only dedicated cycling lanes. Encuriging cycling almost always pays off, in pretty every systematic measurment ever done on the topic. And if you reach Dutch level it pays of a gigantic amount. Its really low investment high return.

Cycle lanes actually look empty often because they are so much more efficent. They have done some studies on paths that were always empty and the threwput is usually not as bad as people think. To be sure the place you are refering to could be totally empty, it happens, but its not the norm even in the US.

Also, of course in a lot of places, specially in the US where they are really bad at cycling infratructure, they believe that all it takes is for one road to have a cycle lane and then magically people on bikes show up. They just want to get in on the 'hype' and were pressured to 'do something'. You need to actually be able to reasonably safely go from A to B between places that are vaguly useful. Dedicate cycling lanes make sense in places where there is no alterantive and you need cars to go resonably fast. But generally its more about your car infrastructure and how fast and dangerous your cars are. Improving cycling always goes hand in hand with making cars less dangerous, and that always pays off.

It takes some up front investment and actual planning, but its not like that infrastructure is worthless after a few years. Cycle lanes once built basically never get destroyed, so putting it in speculatively while having a long term plan makes a lot of sense.