People could move up, because a very large proportion of the labor force was working jobs below their intellectual limits. I think we in the "first world" are a decade or two off the point where this slack pulls taut. At the moment it's mostly experienced as meritocratic good - everybody now has the freedom to reach as high as their native abilities permit. But automation isn't going to stop. The replacement of humans in an economic tier which was fully taut will leave those people with nowhere to go - they can't rise, or they would already have done so. Short of supertech IQ boosters, they're permanently surplus to requirements.
Perhaps eventually this will change. It sounds like you think it will. Why?