EDIT: I was wrong here to criticize the latency since SpaceX's implementation will attack the problem completely differently than traditional satellite internet which has has latency numbers measured in hundreds of milliseconds.
The latency numbers due to the laws of physics through space are lower than the latency numbers due to the laws of physics through fiber when talking about reasonable distances (e.g. new york to london stock exchanges).
Light travels faster in space than fiber. SpaceX's satellites (unlike existing constellations) are low enough that that benefit makes up for the small of extra distance.
To expand on this further, current "satellite internet" offerings are through the use of geostationary satellites 22,236 mi above the equator. The latency to the satellite and back to earth, plus whatever the latency is to get to wherever you are actually trying to go, is significant.
In contrast, the offering that SpaceX has just gotten approval for would use satellites that are about 342 mi above, and the network of satellites would be used to route the connection to a hop close to the destination.
The result of the above is latencies that are actually lower than even a direct fiber connection if the haul is long enough, because connections across Starlink would be at the speed of light (minus the amount of time it takes to process packets at each hop), and the speed at which data is transferred over fiber is some fraction of the speed of light.
Most satellite internet deployments are in geostationary orbit (at 35,786km above the earth), which puts ground-to-satellite latency in the hundreds of milliseconds. Starlink will operate at just 550km, puting the theoretical latency at just 1.8ms. Even if the latency is 30x the theoretical, that's still in line with the latency of copper-cable deployment.
SpaceX's satellites are going to be in low-earth orbit, on the order of hundreds of miles -- you're thinking of traditional satellite internet which is typically in geosynchronous orbit 25,000 miles away. Depending on the number of hops, latency for these new constellations should be in the low milliseconds.
Since they're flying so low, they'll need thousands of satellites to provide wide coverage (instead of one super high satellite that can see half the earth at the same time), but they should be quite high performing.
The Verge article claims 15ms latency, which honestly is really good, even if that's in addition to what you'd get if you were using a traditional internet connection.
Looking at latencies here [1], it’s not that bad. LEO orbit is under 1500 kilometers, adds a bit of lag, but may be compensated by a better route on the other end.
