I think a part of the point is that there is no such thing as the measure of inflation. Every measure of inflation measures some basket of goods; what if I want to buy something else with my inflating currency? Then this measure isn't relevant for me. Also, how can we know whether prices rise due to an increase in the money supply or due to something else? Consider the following example where p, q, r, s, t, u and v all denote a certain good. m denotes the monetary good. At first, the relationship, in price, between these goods is the following:

p=2m, q=0.7m, r=1.4m, s=8m, t=0.2m, u=0.6m, v=4.5m

after a while the prices change and now the relationship is the following:

p=2.5m, q=0.5m, r=1.2m, s=7m, t=0.2m, u=2m, v=4.6m

What role has an inflation in the monetary supply played in the change in prices and what role has factors such as scarcity, difficulty of production, labor costs, etc. played in the change of prices? The answer is it's impossible to tell. Sure, you could calculate an average price change between all the goods, but who is to say that this average stems from monetary inflation and not an increase in wages or an incrase in energy costs, for example?