A person making a lower-middle-class wage and saving 25% of it from the time they're 20, and never facing a financial emergency, will never be "rich" by any causal definition of rich -- let alone among "the wealthiest". In fact, they'll barely have saved enough to retire and live the same tightened-belt lifestyle they lived the whole time.

A penny saved is certainly a penny earned, and saving is better than spending it all immediately. But if you're lower-middle-class and your goal is to "be rich" then you'll need some way to get more money not just spend less money.