The point of "Money can't buy happiness" is that happiness doesn't have a UPC. The connection between money and happiness has tangible intermediaries. You have to spend the money in order to be happy.
The wisdom of it is putting the ball in the hands of the listener.
A lot of times people can get excited just about making money. That's fine because there are so many wonderful things you can buy. On the other hand, I'm sure there is at least an inkling of a further goal behind the idea of making money. No one is trying to be the guy from the parable who dies with a ton of money in the bank (guy has no descendents/will either). Money can be a trap if it is used as a proxy for future desires that are never realized.
"Money can't buy happiness" leads to the question: What is it that you do want?