In reality I think there are more forces extracting money from the wealthy and their effete needs. My example is an airplane. The first class passengers are effectively paying 3x as much for the same outcome. The same is true for ovens and shoes and phones and cars.
I do think it is still very true for tools though. It's nearly always worth getting decent ones, they nearly give better results or are easier to use and last so much longer.
Also Sir Terry Pratchett is a gem of an author and you should read all of his books. I have read through maybe 25% of Discworld and it's the funniest fantasy series ever.
Another way to consider it is through the lens of meritocracy. Consider two poker players of equal skill. Have them play each other until one has lost everything. Run this competition over and over, starting each player with a random stack. Over many trials, the player starting with the bigger stack will win in proportion to the ratio of their stack to their opponent's. Given a large enough ratio, this wealth advantage can begin to overcome greater and greater advantages in skill on the part of their opponent.
In the US, the ratio of the wealth of the top 10% to the wealth of the median has risen from 5.8x in 1963 to nearly 10x in 2022. In the same period, the ratio of the top 1% to the median has risen from 35x to 70x. And the effective advantage is probably much higher, as this calculation does not take into account liquidity: most of a median family's wealth is in their family home.
The premise is just false. The parable might be true when comparing, say, lower class vs lower-middle-class, or lower-middle-class to middle class. But the difference between upper class and middle class is not "spending less money." It's a vastly different net worth that comes from inheritance, building / running businesses, investments, etc.
The boots theory focuses on the costs, but the real difference comes from the income & net worth
Some things are so cheap you can't mess it up. Some things are well-made because the manufacturer made a series of quality-conscious decisions that really added up.
The trouble is the middle, where consumers pay the most attention to branding to make decisions. At the extremes, though, brands matter less.
The poor man wants boots. The rich man wants boots. The man in the middle wants Timberlands or Harley-Davidsons or Doc Martins or whatever.
It is not in any way addressing costly signalling, a completely unrelated behavior where purposefully wasteful and highly visible spending on lower-utility products elevates social status, making low-utility products more expensive and more common than equivalent high-quality products.
Consumer goods have dropped in price, which is good for offsetting inequality. I think the allegory still holds in some other areas (off the top of my head: healthcare spending and renting versus owning your primary residence).
That said, income inequality is probably the much bigger source of unfairness these days.
The books also get better as I get older - I read them first as a teenager and many of the deeper ideas about the human condition went straight over my head.
The way the cult leader in Guards! Guards! manipulates his followers, to give just one example.