I have imagined that the key to scientific progress is to focus on problems that are “within reach”. If that is valid, not sure Harry has good reasons to think that solving death is within reach.
How would “within reach” be defined? One of the themes of HPMOR is Harry using the scientific method to come up with solutions that the non-scientific wizarding crowd haven’t came up with. If the Laws of Thermodynamics can be transgressed in this world, solving death might not be that far-fetched of an idea.