One issue with that logic is when you have people that don't care about being happy at the workplace and just act like they are working. Even if you intervene and try to honestly understand what is making them work the way they do, some of them will feed you with BS.
An option to deal with those people is to just fire them, simple. But that means you are giving up on them. Another option is to have an hybrid approach: those that work great with having happiness as a motivation, we can just continue to foster a happy workplace; for those that don't care about happiness, find another approach, one example would be to introduce KPIs for those specific people and formulate a performance recovery plan if needed, if all else fails, fire them.