Was a simple warning not enough? Or was it a demonstration of power?
Stross never says, but I like to think that the kidnapped population are being used as a early warning and defense system in much of the Eschaton's historical light-cone.
Note the commandments and the existence of human trouble-shooting agents. There is some more discussion of what the Eschaton's agents do and are for in Iron Sunrise which tends to support this view.
I am the Eschaton. I am not your god.
I am descended from you and I exist in your future.
Thou shalt not violate causality within my historical light cone. Or else.
The Herman talking to Wednesday in Iron Sunrise (minor spoilers, nothing that you won't learn early in the book):
I failed to prevent the destruction of your home world. I am worried, Wednesday. Preventing incidents like that is the purpose of my---this component's---existence. A failure to do so suggests a failure of my warning mechanisms.
I am a component of the Eschaton. The Eschaton preserves global causality within a realm approximately a thousand parsecs in radius. It does so by transmitting information back in time to itself.
I receive orders form deep time and execute them knowing that the descendent state vector is going to exist long enough to order issue these orders. If I do not receive such orders, then it may be that the events are not observable by me. Or my future state vector. This situation may occur if the Eschaton is disrupted or edited out of the future time-line.
It isn't stated in this book but there is evidence in Iron Sunrise that the Eschaton has enemies that it fights with the same causality breaking weaponry that it has denied the near-future humanity. It stands to reason that the scattering of the earths population across the galaxy is a good safety measure. However, (near-) divine beings that don't give explanations of their unfathomable behavior is a common technique in any work of fiction. I hope that the series continues...