There are a few reasons that come to my mind that could explain away one of the many plot holes from Defenders.
So, what is that earthquake?
Bear with me, even though this is not the original question, it is connected to the whole 'New York will collapse' trope (maybe not exactly a trope, but i struggle to find another adjective).
- When the Hand find the skeleton, there are certain things I think we can safely assume. 1 - The dragon skeleton holds the key to the Hand's immortality, 2 - there is magic involved. Given the point that there is obviously some supernatural element involved with the dragons (one gave Danny a glowing super strong fist), i think we can also safely assume that something that disturbs the 'peace' of the dead dragon might be more catastrophic than its simple physical reaction. So, when they first find the 'gate' (the wall), it sends a tremor through the surroundings.
Subsequently, the bones being dug up and ground would presumable cause a terrible loss in the 'chi' of the area, causing a collapse. Also, let us not forget that excavating massive bones under a city might be geologically daft too - that one is for a geologist to answer.
Jessica's bff Trish Walker receives perhaps the most crucial bit of
intel, when a geologist calls into her talk radio show to dispel the
notion that this anomalous event was a "shallow" earthquake caused by
a fault line under the Hudson. According to the caller, shallow
earthquakes can still run up to five miles deep — whereas this
disturbance originated less than 300 feet underground.
this from https://www.bustle.com/p/what-caused-the-earthquake-on-the-defenders-the-natural-disaster-probably-wasnt-natural-at-all-76747
So, I think we can be fairly certain that the Defenders focus is on the supernatural dis-balance. Finding and trying to break down the Wall (without the fist) caused the tremor, and the removal of the dragon bones would be disaster.
As a result, collapsing the tunnel, and bringing down the building prevents the hand from removing more of the bones (at least for some years - till they can dig again if they survive). This, then keeps the supernatural balance or chi intact and lets the sleeping dragon bones lie along with all of New York.
Why would New York collapse? Answered above ^
Is it that the Hand are deliberately destroying the city as a separate venture to the extraction of the skeleton, or is it an unintended but known side-effect?
The Hand were definitely destroying New York, but as an intended side effect. Remember Gao (or was it Alexandra telling Elektra) says the Hand have been destroying cities for ever.
If the former, why are they destroying New York?
Cos that's what they do, according to screen rant, and the show
They masquerade as various companies and corporations, transferring
assets around in an ongoing front with Reid as the recurring CEO.
Stick, whose rival group the Chaste have been battling the Hand for
decades, points to two major historical events, the volcano in Pompeii
and the nuclear meltdown in Chernobyl, as having been caused by the
Hand to access these fossils
If the latter, why was New York not destroyed when the skeleton was crushed?
The skeleton may have been crushed, but let us remember it has been buried for centuries, right? Right. So, it is still encased in a bunch of earth. If more earth really falls around it, will it be crushed? Or maybe just rearranged? Either way, if Matt can make it out of there, i'm sure the bones are fine - and undisturbed (in the sense that they aren't being used as supernatural immortality juice), hence keeping New York safe.