Regarding the horse example, there US horse population is 9 million. The demand for horses never went away despite automation and has remained steady. If one tried to extrapolate the early 20th century horse population trend to the future, there should presently be no horses alive.
Although the labor force participation rate is falling, the total labor force size has not (although it has flattened in recent years).
Rather than the total elimination of jobs, a more probable concern is the bifurcation of the labor force by IQ, with those with an IQ below a certain threshold barely getting by, stuck with low-paying jobs that barely pay ends meet. Due to economic and technological factors, this IQ threshold will likely gradually keep rising. http://greyenlightenment.com/two-nations-within-a-nation/
This is why the decline of manufacturing jobs has not hurt the overall labor market size, because such semi-skilled, medium-IQ jobs are being replaced by service sector jobs. However, the pay for these jobs is not as good.
Often what happens is the new technology will coexist with the older one, as the bank teller example shows. Other times the implementation is so slow that it is not a concern. I remember in 2007 McDonald's, Jack in the Box, and other fast-food chains began to install self-order machines, but the adoption was really slow, the machines were often broken, and the machines didn't replace the role of the cooks and cashiers. People needed help using the machines, necessitating staff. Same for those food store self-checkout machines. Rather than the machines eliminating the cashiers, they coexist. Some people like machines, but others don't. Machines break and someone has to supervise the machines in case someone needs help or tries to fool the machine by imputing the incorrect weight or item.
Overall, I am not too worried but I can see some cause for concern. Regarding post-scarcity and UBI, entitlement spending has been on an unstoppable rise for the past 50 years. We're already headed in that direction. SNAP, medicaid, disability, and section 8 housing is pretty close to a UBI and post-scarcity. The future is one where the government assumes a greater paternal role in helping those who are unable to keep up with an increasingly competitive economy.