You probably won't be using Landsat for disaster relief. Not only is the repeat cycle too slow, the spatial resolution is too coarse to identify damage.
Drones are an option, but they don't cover a very large area. If electricity is down, internet and recharging can be an issue. Sometimes they're good, but for more specific issues like "how many floors collapsed on the building at location X?"
Aerial is an option (and probably the best if you can get there). High resolution satellites can work too, but only if there are no clouds.
So, it depends on the context. And disaster response is one of those fields where they always have GIS people.