There is no obviously appropriate way to measure this, even in theory.

It's hard to discuss these things without getting into all sorts of overly controversial topics, but I definitely disagree that there are no obviously appropriate ways to establish whether this, so to say, skew of the status distribution is increasing.

Admittedly, these are fuzzy observations where it's easy to fall prey to all kinds of biases, but there is still useful information all over the place. You can observe the level of contempt (either overt or more underhanded) that people express for those below their class, the amount of effort they invest just to make sure they're insulated from the lower classes, the fear and disgust of mere proximity to anyone below a certain class, the media portrayals of people doing jobs at various percentiles of the income distribution, the reduction and uniformization of the status criteria and the disappearance of various sources of status available to those scoring low in wealth, fame, and bureaucratic rank, and so on. Of course, my observations and interpretations of all these trends may well be biased and inaccurate, but it's certainly incorrect to claim that no conclusions could be drawn from them even in principle.