I suspect this stereotype may have a signal-to-noise problem. Consider that many men who buy a corvette at mid-life may have wanted one since their childhood, and mid-life happened to be the earliest point at which they could afford one.

Exactly this. “Mid life crisis” is just a fabricated pejorative meme. The reality is that for most middle class men, they can only afford to spend money on long sought after expensive hobbies once they hit midlife.

Ok, evenso, given that testosterone goes down for many, this effect could exacerbate their desire for repressed purchases.

Depression causes you to engage in behaviors which reinforce your depression, and I would expect low-testosterone would work similarly. In other words, the men seeking status goods are not the ones suffering from low-testosterone, but rather the ones whom are already high-testosterone.