Let's look at numbers. NYC->LDN great-circle distance is 5576 km. At altitude, that is (3959+547)/3959 * 5576 = 6346 km. Idealized path is thus 547 * 2 + 6346 = 7420 km. (Actually a bit less because the path is part of a polygon, not an arc.) Non-ideal path, for satellites not directly overhead, is more like 7900 km, worst case more. Still, transit time, light through vacuum, is <28 ms.
Compare to fiber. Best ping time is 76 ms, or 38 ms one way. So, our budget margin is 10 ms. Suppose, instead of a direct downlink, packets are dumped to a nearby hub and carried via 1000 km of fiber to the destination, with various routing delays, adding 5 ms, leaving a 5 ms lead, 5000 microseconds.
In finance, we say a microsecond is an eon, a millisecond an eternity. That is because in a microsecond we can do >1k multiplications. 5 ms is time for >5M multiplications, many more than needed to evaluate a position and choose a response.
The only routing choices are which satellite to uplink to, and whether to forward or downlink each packet. Whatever choices are made don't need to be re-evaluated more than per second. Packet queuing delay can be negligible; modern switching equipment will start forwarding a packet while the rest is still arriving; this would happen when forwarding via laser link.
The latency advantage for New York/London/Frankfurt <-> Singapore/Tokyo/Hong Kong would be even more compelling.