So here’s a thought for you.
According to a recent visit to the German History Museum, at its apogee, the Roman army had 400-500 thousand troops to protect the empire’s 50-60 million inhabitants.
Today, the United States military has ~1.5 million active duty personnel and a similar number of reservists (source) to protect its roughly 300 million strong population.
Interestingly, this is roughly the same ratio of 1 soldier per 100 citizens. This is only two data points and does not a trend make, but I wonder if there’s some sort of permanent ratio that is simply the cost of being the world’s policeman – and it’s independent of technology/politics/history/etc.