There was not enough space for cars, we tore down entire neighbourhoods and blasted through bedrock to create highways.
There is not enough money to fund a moon program or fix climate change, but when time came to bail out the banks, if you stacked that money as 1-dollar bills it would reach the moon.
There is not enough money to Fusion research, but our fossil fuel and airline subsidies in one year are greater that all-time fusion research budget.
Priorities.
The prioritization back then was that "those people" don't matter. That is how those were build.
Especially in the US there is plenty of space you can take away from cars, both lanes and parking.
The Netherlands did not knock down and rebuild Amsterdam to build bike paths. They took space back from cars.
The first is car centric, with lots of roads and deep set backs. These cities are amenable to bike and public transit transformation in terms of space, but usually have political resistance to change. These cities will be the easiest to add extra bike infrastructure to, once a political mass is reached. My current city is like this, and the current bike path master plan is trying to add enough paths for 96% of the city to be near bike infrastructure (currently it’s 10%).
The second category are really dense, and do not have the space for any extra lanes. But these cities dedicate a huge amount of space for parallel parking. Theoretically the city could remove parking for bikes, but practically this means purposefully pricing people out of car ownership, which is obviously unpopular. These cities should focus on public transit, which is by and far the most space efficient way to move people. For a lot of these cities this is less about installing new lines, which is expensive, but about making the existing system feel cleaner and more dignified. It will always be hard to make improvements when even the crappiest sedan is considered a step up from taking the subway to work.
The key is that cars don't belong in most places anyway. A residential street can easily be design as a 10mph one way cobblestone road with calming measures, freeing up the "other direction" side of the street for a 2-way bike lane and expanded sidewalks. Larger roads can be redesigned similarly for bike/transit with cars filling in particular niches like delivery of bulk items, etc.
It also costs less to maintain, kills fewer people, massively reduces healthcare costs improves the local economy and is far nicer to live next to.
There is plenty of money, most places are just directing it to yet another road widening project that will make things worse.
In any case, it's pretty much a non-starter to prohibit at least conventional bikes or pedestrians even though, on the more crowded and narrower paths, I'll avoid them during busy times as a walker.