That's actually a really cool concept.
I'm going to start off by saying I strongly believe that money buys happiness. Not directly, but it leads to things that make us happy.
I was actually marked down on a paper in high school just because I told the teacher that, when she expected the unanimous 'money doesn't buy happiness' from the class lol. Anyway.
We need money for food, shelter, and (to a lesser extent) clothing. Money leads to transactions that could lead to happiness - getting married? You're likely going to need cash for an engagement ring bro, and that could lead to lifelong happiness. In a long distance relationship? Gonna need money for transportation because I doubt you're going to walk or bike (bicycles also cost money) for 600 miles. Hobbies can also cost a lot of money, and for many people they're the source of relaxation and happiness.
My point being, if happiness were the source of currency, it'd be a continuous cycle of being happy > getting 'paid' > buying something or paying something off > being happy about that, etc.