For the above example, one province will have 4 mini-counters in it and your brain will have to go 1+2+1+1=5 to figure out how many divisions are in that province, whereas you would be able to estimate the amount of divisions from a stack of counters at a glance by judging the stack's height.
I'd hope that anyone playing the game would be able to count to five.
More seriously, you're not comparing like with like. You're complaining that it will take more effort to get a precise count than it would to get a guesstimate with the old tiles. In reality, even if your arithmetic is poor, you can get as good an estimate from the number of different types of division and how many of each as you could from guessing the height of a stack, and if you wanted an accurate count it would take longer to count the tokens than to do a quick sum. This also ignores the fact that you only knew what the top token was. If a stack has six tokens in it, it makes all the difference in the world if that is an armoured and five militia or five armoured and a mechanised.