And the synthetic cell doesn't need to do anything about separating genetic material between daughter cells because it's just free-floating DNA that is likely to be in both parts. Right?

The complexity is certainly awesome, however there are all kinds of "free lunches" that we can take advantage of here, I'm paraphrasing (and glazing) Mike Levin here - when you work with biological systems, you are handling an agential material that naturally expresses itself.

I suspect that, once scientists lean more into the right kind of communication with these systems that many substantial leaps forward will be made. I am very excited about it too, mostly because I think it has the potential to positively impact how we see ourselves (humans) in the natural world.

Somewhere here is a science fiction story that humanity is too inexperienced at synthetic biology to create sophisticated forms for manufacturing and have to result to the equivalent of bashing proteins together to make inferior biology to some future humans or other species.