The analogy is like pointing out that you can have a robot vacuum clean your floors every day. Before the robot, you'd do it maybe once a week, just no time - "too expensive" to even think about doing it daily. The robot makes it happen all the time for a tiny, tiny fraction of the cost.
Edge cases handled automatically by a human doing the task (getting stuck), means for the robot case that manual interaction is still a thing. Occasional, yet not making autonomous behavior, human free time.
Emptying the vacuum bag is a thing too, some things are not abstracted away.
Every time you add an entirely to a task, the task time goes up. Coordination is a time cost.
The savings you suggest are often not so stark. Not even for our friendly vacuums.
For sure. Still much cheaper than vacuuming every day.
> getting stuck
I appreciate that this is a function of the specific environment and robot you buy, but as a personal anecdote, this doesn't happen to me in practice. There was a setup cost, but once that was done, it doesn't get stuck.
> Emptying the vacuum bag
Not that frequent at all, considering that daily vacuuming keeps things remarkably clean and thus little is added to the main bag in the docking station each day. This is also far less work and far more preferable than doing the vacuuming myself.