yes, that's definitely part of it. As Adam wrote: 

The number and cost of disasters are increasing over time due to a combination of increased exposure (i.e., values at risk of possible loss), vulnerability (i.e., how much damage does the intensity (wind speed, flood depth) at a location cause) and that climate change is increasing the frequency of some types of extremes that lead to billion-dollar disasters (NCA 2018, Chapter 2).

As far as I know, no one has done a more detailed attribution analysis--trying to determine how much each factor (exposure, vulnerability, and disaster frequency/intensity) has contributed to the observed increases in billion-dollar disaster events. But if they did, they would have to account for all those variables you mentioned, and more!