And this... this is why we don't do that thing. If you have your heart set on testing breakers, build a rig that flows 3 volts AC at an adjustable current. The breaker doesn't care what the voltage is, and it greatly reduces the energy involved in destructive failure. Anyway an even easier way to test breakers is to replace them with new stock. A new breaker is $5.
Two possibilities: a) the breaker malfunctioned and did not trip, or b) the breaker worked within its specification and exposed a flaw in the supply side wiring. Let's look at each in turn.
The breaker malfunctioned
That might happen because of severe age of the breaker or prior damage from past overload.
However, three lines of breaker are of particular interest, because apparently in the 1960s, UL's inspection regimen was a bit slack and was generally done in the manufacturer's own lab. Several breaker manufacturers discovered they could cheat the test like Volkswagen, and they did. These include:
Challenger -- the Type C and Type A breakers. However, the panel enclosures and buses are perfectly fine, and are now used for the BR type, the most popular brand in America. Indeed, BR breakers are cross-listed type C or A, and thus are approved for Challenger panels. Change the breakers you're all set.
Federal Pacific - aside from cheating, they also have a problem in the 240V 2-pole breakers. Their "common trip" mechanism (intended to trip both sides) tends to bind or tram, so neither side trips, and the breaker stays on. Federal Pacific also has an innovative bus design which proved to be a disaster, so the panels can't be saved and must be wholly replaced.
Zinsco also has problems with failure to trip, and again an innovative but faulty bus design, condemning the panels to complete replacement.
With Federal Pacific and Zinsco, third parties are manufacturing replacement breakers for those panels for a king's ransom (e.g. $50). These breakers have been tested extensively by consumer watchdogs, and are found to be even worse than the originals. And they do nothing about the bad bus design.
With Challenger, the panel is fine and BR breakers can be used.
Breaker worked within its specification
Let's take a look at a typical trip curve for a modern, "miniature molded case" breaker of the type used in home panels. Don't mind my recycling, the markings are by ThreePhaseEel for another answer.
How to read it: Horizontal is multiples of overload, and it's a log scale (so each major line is 10 times the last one). Vertical is time in seconds, and again a log scale. Log scales make the chart possible to fit on one page; without them this chart would be a couple of acres lol.
The grey area is all about manufacturing tolerance, as not everything is precise (and certainly not for $5).
Let's read an example. Our overload on a 20A breaker is 40A, or 2 times. So we go to the 2x line along the bottom and go up. We find that it enters the gray area at 9 seconds, and exits at 35 seconds. This breaker, if overloaded to 40A, will trip in 9 to 35 seconds.
We can work it the other way too (again Thanks ThreePhaseEel): if it tripped in 1 second, what does this mean? Find 1 second on the vertical, go across and the gray area starts at 4.5x and ends at 8x. So 1 second trip means the overload was 4.5 to 8 times breaker rating.
Getting the hang of it?
You may notice that an 8x overload (or any over 6x) might be instant. And above 10.5X, all trips are instant. (instant being within 1 cycle or 0.016 seconds). Why? This is a second mechanism inside the average breaker, called magnetic trip aka "instant trip". The manufacturing tolerance is between 6x and 10.5x of breaker rating, it must trip above 10.5x and might trip above 6x.
You didn't mention the amp rating of the breaker which tripped. But multiply by 8, and that says how much current could flow before the breaker trips in 1 second.
If the breaker was 20A, that should have limited current to 160A, which a 200A service should have been able to handle (continuously all day all night, e.g. for EV charging.) That would suggest damaged wires in the service, which would be the power company's problem. It would not explain the meter meltdown, as that too should effortlessly handle 160A for one second.
Even a 30A breaker (240A at 8 times) would surprise me if it damaged 200A service wiring.
A 40A breaker (320A or 50A breaker (400A) could be more trouble, though. This is a good lesson not to oversize breakers.
ProTip™
: testing a breaker by causing a dead short just is not a good idea. Especially if you don't know anything about your panel as there are some (as @Triplefault was alluding to) that are known to not always trip properly, thus being labeled "fire starter" panels.