A simulacrum of a caster can use magic, or this line would not make sense:
[...] nor can it regain expended Spell Slots.
But a caster can only have one simulacrum:
If you cast this spell again, any currently active duplicates you created with this spell are instantly destroyed.
The simulacrum is not the caster, it is a different creature. Since it has spell slots and the statistics of the caster (Including the spellcasting trait), it could cast simulacrum too. And the duplicate created by the simulacrum's casting is not created by the caster.
So, here is the scenario:
Suppose Anne, a caster [class redacted] can cast simulacrum.
Anne creates a simulacrum, and names her Betty.
Anne commands Betty to cast simulacrum, using a strand of Anne's hair. Christine is created.
Anne then (maybe after a long rest) casts simulacrum (of herself) again, creating Dorothy. Betty is Instantly Destroyed.
Since ongoing spell effects do not depend on the caster to continue on, This may leave Anne with Christine and Dorothy, both able to cast simulacrum.
Is there any flaw in the reasoning above? Is it allowed by RAW?