What am I missing?
That it's a timing issue.
The S1/S2 modes are "dumb"; there's no communication between the camera and the flash going on. A simple sensor on the flash detects when a flash burst has gone off, and then fires the flash. As you noted, S1 fires on the first burst sensed; S2 on the second burst sensed.
With flash, the camera cannot meter how much light flash adds in the scene until a flash burst is in the scene. That's why TTL uses a pre-burst.
But that TTL metering pre-burst also trips the sensor. If you're using TTL, and your flash is in S1, it trips the flash early: on the preflash, not during the main burst.
...all s2 mode really seems to achieve is to screw up the metering by making the main flash far bigger than the camera expects.
S2 doesn't affect the flash power at all. Only the timing of when the flash fires. S1/S2 are always manual triggering modes where the power level on the flash must be set in M mode, directly on the flash itself.
If you want to use TTL power control over an off-camera flash you must use a "smart" optical or radio triggering system, or 3rd-party TTL radio triggers that can fully communicate with the hotshoe of the flash.