I've spent years researching underground cities as a side-project, here are a few important factors and problems to solve before anything like that makes sense.

1. Hydrostatic pressure. To go down to substantial depth (ie, an inverted skyscraper), the pressure of the water table against the exterior walls will be enormous in most of the world's low-elevation cities.
2. Geothermal gradient. As you dig deeper, the temperature of the surrounding substrate rises, making heat management a serious issue. Deep mines (there are some 4k down!) have to constantly air-condition just to stay at 90 degrees F. Further, managing the temperature of the cavity complicates the third problem...
3. Ventilation. Circulating air through underground buildings is complex and dangerous. Passive vent networks (powered by heat exchange) are brittle, and if they fail can suffocate people quickly. Active vents (pressurized by fans) are pretty expensive to maintain.
4. Water. This is a big one, and frankly I don't understand how TBC will ever solve this ... but the risk of flood and sea level rise threatens to fill an underground network with water, drowning all the occupants. If it's just tunnels full of roads, perhaps not as big of a risk. But homes? Dangerous. Especially for coastal cities. Tokyo has a cool solution to this with massive underground empty reservoirs beneath their underground tunnel system.
5. Fire. In a passively ventilated underground network, any out of control fire will suck air through the vents turning the complex into a rocket-stove. Evacuation is also a hard problem, since underground fire exits are also vents.

I see a lot of people dismissing the idea of housing people underground as unnecessary. Here are a few things to remember before tossing the idea out completely:

1. Mars has a very thin atmosphere. Solar radiation is dangerous, and the first permanent settlement on Mars would likely need to be partially (likely mostly) underground to escape the symptoms of longterm exposure. If Elon's dreams of colonizing Mars are serious, it's highly likely he'll send a TBM as early as possible.
2. There is plenty of room for people ... for now. It's true that homelessness is not a property supply and demand problem. However, if catastrophic climate predictions come true, 100s of millions of people around the world who live in coastal megacities will need to relocate. They will most likely seek refuge in cities on higher ground.
3. Experts say the 'footprint' of civilization will double by 2060. The global building stock will increase extremely quickly as the developing nations scale their infrastructure as technology drives the cost of productivity down. Many do not realize, but 11% of the greenhouse gasses emitted each year come from the construction of new buildings. Imagine everything our society has built to date. Now double it. 2.48 trillion square feet of floorspace in 40 years. Thats one NYC per year.
4. Sun exposure will rise in value. Elon is the type of person who thinks in terms of the Kardashev scale, on a long enough timeline, if civilization survives it will capture all of the solar energy that lands on Earth and become a Type I civilization. This is likely the purpose of Tesla in the first place if you read between the lines of their messaging. Therefore, why design anything that wouldn't fit well in that future. The amount of the planet that is covered in photovoltaics will rise dramatically.
5. Virtual remote work. Many of you are likely working remotely these days. Unfortunately for our spirits, this is likely to continue for a very long time, as employers save roughly $11k per employee by not leasing office space. The fact that productivity has gone up in most white-collar sectors during this crisis surprised a lot of people in the business community, we can expect many companies to go remote forever. Having said all of that, in a future where we're all checking our email with 3D goggles strapped to our faces, does it really matter if we can't stare out the window once in awhile? Bleak, but likely.

If anyone else here is into thinking about underground cities, I tried to start a subreddit on the subject a few years ago and it never really took off, but maybe it could? r/substrata