I think that it is a function of the laws of the country - for Thailand they ask to see your passport but don't copy it.
Also, it seems like a procedural thing that can differ between chains. Hyatt in the US rarely asks for ID but Starwood properties usually ask to see an ID (Driver's License).
Since this isn't really an issue exclusive to Hyatt, I'll move it over to Travel Buzz so that hopefully more people will give you comments.
peteropny - co-mod - Hyatt