Can I have a... (spoilers)

[Valence]

Is it really reviving if the regulator simply copies your memories onto a new soul?

Since the story has made pretty clear that what matters and constitutes a person is memories and not the soul (which is just an energy vessel, whether being cleansed in the aetherial sea or artificially), then yes?

You know regulators only work by eating the souls of people who were removed from the life stream. This means in a world where reincarnation is real you are perma killing someone by using a regulator.

You're not killing anybody by using souls stored within regulators. The real issue that the story brought up with Alexandrian society is how unsustainable their system is, and how it draws souls away from the aetherial sea and the natural system without giving back (and also required even more just to keep the endless/matrix online).