In my experience, that isn't completely true. Sure, as you get more financial committments, you start needing the money more.
However, having extra money makes so many things less stressful. When I was younger and poorer, car trouble was a huge stress. Did I have enough money to fix it? What was I going to cut out? Would I wreck the car, costing me more money, if I keep driving it?
Now, I just take the car to the shop and don't even think about it. Hungry and see a good restaurant? Just go. Get in a minor accident, or get a parking ticket? No big deal, doesn't ruin the day.
I mean, money certainly is still a factor in decisions, but there are a LOT of decisions that cost a small enough amount of money that you don't worry about it. Everyone has a level where, if things are cheaper than that, they don't worry about it; as you get more money, more and more things fall into that category.