If we have no memories or knowledge we can keep. Then the existence of reincarnation is completely irrelevant. It's not essentially us that move on then.
Without a religious connotation to it, it is meaningless, yeah.
But if you believe in say, Hindu/Buddhist Reincarnation/Rebirth, then while you might not bring your memories or knowledge along into your next life, you still bring your soul/karma.
So, your actions in your current life (and previous lives which you can't remember) impact on the events in your current life/next life.
So a bad person might be reincarnated into a lesser animal, or be reborn into a person who suffers a cruel life of disease and illness or tragic death.
There's a documentary I watched a year ago, where an Anglican priest travels meeting people and their beliefs on the afterlife. And he meets a lot of people in Indonesia and the surrounding areas who suffered in the 2004 Boxing Day Tsunami, and their beliefs on reincarnation/rebirth, and how they cope with the idea that their God(s) let this event happen to them.
But I'm having difficulty finding it. If I do, I'll send you a link. It's pretty interesting.