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.
it's certainly incorrect to claim that no conclusions could be drawn from them even in principle.
I wouldn't claim that, my claim is that there can't be one formula specifying what you want to measure, so for reasonably similar societies like this one and that of fifty years ago, you can't draw conclusions like that. If one looks at all the equally (in)appropriate ways to measure what you're making claims about, the modern USA outperforms 18th century Russia in enough ways that we can draw conclusions. I'll elaborate a bit on your examples.
...fuzzy observ
From Mike Darwn's Chronopause, an essay titled "Would You Like Another Plate of This?", discussing people's attitudes to life:
Conclusion, graphs, and references in article. As usual, I recommend reading Chronopause.com as Darwin has many good articles; to quickly link a few: