If you actually think about it, the concept of sleep (that your body just decides to shut down for several hours every night) is pretty weird. amirite?

It's inaccurate to say the body "shuts down" every night; the brain is still very active during sleep (by some measures, more active than during waking hours). And the idea that an organism needs rest in order to rejuvenate/heal/grow actually seems quite intuitive to me. What is weird to me is that we haven't yet pinpointed the exact mechanisms of sleep that make it necessary.

No, it's like putting the phone to charge up during the night. It can't work forever.

I get it. It's not weird that your body has to rest. OP likely means that its weird how your body assumes some sort of unconsciousness in order to fully rest.

I would say if you don't think about, it seems pretty weird. Once you start thinking about it, it makes a lot more sense.

It makes me feel like I'm a robot.

How is it weird? Most people work their asses work during the day, so it's perfectly reasonable that we need to rest each night (not "shut down", necessarily) before getting up and doing it all over again.