Lots of things are expensive though, so it has to be more than that.
From all psychology signaling is most powerful when it shows expensive resources spent on unpractical, useless things. As the peacock tail.
Spending a hundred bucks on something useful is not a signal showing wealth; but lighting a cigar with a hundred dollar bill is such a signal.
Being seen with, say, an expensive computer is less powerful wealth signal than being seen with an exactly equally expensive ring; the computer might be (even if it isn't) practical, but the ring states "hey, I can afford to waste money, so if you don't then obviously I'm of a higher social status/pecking order than you".
It's better if everyone in society can agree on the same signal to use. Otherwise it's too hard to verify.
That's true. But why do diamonds have high social status? Because they are expensive. They are a reliable signal of the wealth of the man. Social status is a proxy for actual wealth and power, and thus the probability of wealth and power for the woman's potential offspring.
Unfortunately they have become such a strong signal that people without wealth to spare feel compelled to over-spend on them. Like a peacock's tail.