Letting the children live would give you the problem of a vengeful (and rightful) heir in ~10 years' time. Exterminating the Romanovs completely would seem to b

Letting the children live would give you the problem of a vengeful (and rightful) heir in ~10 years' time. Exterminating the Romanovs completely would seem to be a pragmatic choice, given the real power of the Tsar's legend. It's not clear that life imprisonment would have turned out very well for the Romanovs, given the lives of other political prisoners under the Soviet system; and simply freeing them would allow them to join their family members in Europe, garner support and prepare for an invasion.