So, let's not fool ourselves with predictions. We are notoriously bad a predicting long term trends.
PS: the analogy with horse is wrong in so many ways (because horses are not humans and cannot adapt like humans) but this would be another topic altogether.
The problem is that throughout human history the demand for unskilled labor has exceeded the supply, and that has been the foundation of our social contract: work, and you eat. Don't, and you starve. But some day soon, technology could make that assumption no longer true, at which point we could have big problems unless we radically rethink how our society is organized. That is something we humans have historically not been very good at.
Look back also in the early 1900s where all major newspapers were proclaiming the end of world and massive famine if we ever reached 1 billion people on Earth"
If we all put our backs into it, we can make sure that we need at least that many.
We just have to write really bad documentation and really sloppy code, which lot of people believe we are doing already.
With a bit of effort maintaining the software being written today will become such a monumental task that no Soft Eng will ever be out of work for millenia to come.