The problem is fundamental and serious, what to do when a growing number of people have literally nothing valuable to contribute to an economy. But horses aren't a good analogy to shed light on it.
Horses are more analogous to steam engines than people, in their historical function on the economy.
Horses are a bad analogy if you want to prove that AI wont take over most jobs.
They are however a great analogy if you want to see how technology once it reaches a certain point renders biological beings sub-par useless as part wealth creation.