Rich, classy people are NOT buying Coach. At all. Their bags are dirt cheap and are made out of shitty material.
But I get your point. Middle-class high schoolers divorced moms in the suburbs will spend a child support paycheck on this because it has the logo all over it and the SA told her it's a popular bag. Richer people go for far more subtle designs on bags with a richer history and better build quality.
And they most definitely don't go for the same brands. Poor/middle-class people stick to the gigantic, over-marketed brands with designs that famously emphasize logos like LV or Gucci, or brands that are not HF at all but just look like it at a cheaper price like Kors or Coach. Richer people stick to brands that may be as popular, but are far more subtle, harder to find and wayyy out of a middle-class person's budget, even when that budget is "my entire child support paycheck" - Hermes, Chanel, Dior, Versace, Saint Laurent, Goyard, etc.