You’ve probably thought about it already, but if you tear down the old roof, you'll likely have to fix a new layer that the insulation and similar materials rest on. In that case - will it have a different density? Breathe less? It's worth considering, depending on what the intermediate floor looks like.
During demolition, it might be difficult not to damage the battens needed to attach the new roof to.
I would leave the old one in place, any time. As long as it’s whole and clean without strange spots that need investigating.