I suppose the limit might be quite high, but I've never seen it discussed at all.
(1) Cost. Building roads and highways inflicts both huge upfront capital costs and maintenance costs. A typical highway line has a throughput of 2,000 cars per hour. (2) Real Estate. Building the level of roads necessary to meet induced demand+ would take up an extremely large amount of land that can only be used for vehicles. (3) Local Roads. Local roads can only absorb so much capacity and they have functional throughput limits. If you wanted to make them faster, homeowners couldn't have driveways.
If you really wanted to, you could possibly make a city where driving is king and there is effectively no congestion. It would just be absurdly expensive and hostile to everyone who doesn't have access to car.
This is exactly what has been done in most of North America, except for the "no congestion" part.
I'm not sure which one would be quicker: having a really long access ramp (long because of the tunnel's depth), or having to wait in line to board an elevator that moves quite slowly.
This reality is also frequently ignored in the housing conversation when people advocate the solution to high prices is to simply add more supply, as if it's a given that supply could be created fast enough to overtake demand. I find that no one really ever does the work, taking into account the friction of real life on supply creation, to figure out if that's likely to be the case.
Musk's propositions should and will coincide with years of statistical analysis before actual implementation to prevent exactly what you're talking about. Hyperloop could be to the detriment of a lot of cities, but that doesn't mean there aren't implementations that can improve transportation time, congestion, and quality of life. The attitude that pursuing futuristic transportation technologies will hinder ALL cities seems detrimental to human progress. What brought about our "proven" public transit systems, like subways, to begin with?
Developing Hyperloop or the Boring Company doesn't need to mean replacing current infrastructure or stopping municipal efforts. It means we could put our brightest engineers towards some of humanity's most annoying problems (https://www.wsj.com/articles/SB913090787638355000), forcing them to pay attention to municipal data along the way. If analysis indicates that tunnels would be detrimental to New York, then by all means, let's not build tunnels in New York. But if other analysis indicates that Los Angeles, a city incredibly dependent on cars for transportation (http://www.smithsonianmag.com/history/nobody-walks-in-la-the...), might actually benefit from such an idea, we should pursue it.
Don't be so quick to reject an idea before proper analysis has been done to understand the impact. It's the innovative ideas that end up actually improving humanity, and believe it or not, a lot of the things we consider to mundane today, sewers, subways, roads, skyscrapers, were at one time innovative and new.
Before pursuing innovation, it's worth knowing what came before you.
The sheer number of people who speculatively re-invent bus lines when thinking about what Uber/Lyft could do in the future is proof of this.
In other words, "You can't build more roads. If you build more roads, people will drive more, and then there'll be more cars on the road. And we can't have more cars on the road. So you can't build more roads."
Am I missing anything?
The Boring Company's "cars in tunnels (maybe on sleds?) idea", which Musk is following up on, is even more dangerous and has worse impacts on cities. For one thing Induced Demand is a well studied, proven fact, so we know that the expansion of road infrastructure will incentivize more people to drive and create more traffic in the long term. This means not only that these tunnels will inevitably get as full as the roads above, but more importantly that the broader road network of the region will be severely negatively impacted by the new traffic induced by the tunnels. This is precisely the wrong solution at a time when municipal governments are more interested in reducing car use, because they understand very well the benefits in pivoting toward creating denser, more walkable, cities and are currently engaged in making this shift.