We can be absolutely certain that the possibility of reinstating the monarchy would be very bad for lots of Jewish children.

Shooting a specific Royal lineage doesn't change anything about the possibility of reinstating the Monarchy. The white's didn't evaporate after the executions in the same way that the coalitions didn't evaporate as soon as soon as Louis XVI got the chop, and the House of Windsor doesn't quake at the thought of the current Jacobite pretenders. . The notion that the fate of the revolution hangs in the balance of Alexei's life is some grade A great man theory nonsense.