Does anyone know how important hot staging is?

It seems to give the booster a real kick - what's that do to turbo's and fuel movement?

You've got hot exhaust onto cold cryo fuel tank header?

You've got to carry more mass in terms of protection for the tank?

Is doing MECO and then push and then get 100 yards apart or something before second stage / ship engines kick on a big enough penalty to justify all the extra complexity?

All the velocity you lose in any kind of throttle back is velocity you never get back. It hurts you the entire rest of the flight.