Here is a list of the 10 largest earthquakes measured since 1900. We have about 1.3 Million earthquakes of magnitude 2 to 2.9, and 134 of 6 to 6.9 per year. But most of them happen in the sea, in deserts or far from cities.
But we have an increasing world population, so the number of affected persons can climb over the century. We have increasing numbers of artifacts which can be damaged, and therefore increasing damages in form of costs, while predictions of earthquakes get better, and the number of EQ-resistant builduings increases, which meanwhile lowers, but doesn't compensate, the damages.
And we have an increasing number of stations which measure EQs.
Numbers of USGS and GFZ Potsdam
Oh - I forgot the answer: :)
For the last 100 years, there is no increasing number of EQs. But the timespan of interest might be choosen to fit the claim. You could watch just for a few weeks and EQs stronger than x.
I guess it isn't possible to count prehistoric earthquakes today.