It’s funny you should mention automobiles, because it’s actually a pretty good analogue. Sure, the car itself was probably not invented with some kind of political goal in mind, but the complete redesign of many cities to be car-centric, because “cars are the future!”, making people dependent on cars and destroying neighbourhoods to build highways along the way, was (and continues to be) very much a political project.
As for the “paradox”, whether or not AI is actually capable at replacing jobs is not that important. What matters is whether or not the pretense that it can (and therefore the pretense that workers don’t have any leverage), can be kept up for long enough that the networks workers use to consolidate their leverage, like unions, fall apart. As an example of a similar strategy, see Elon Musk promoting the Hyperloop to prevent the construction of high speed rail.
Certainly, in the same way that failing to catch a bank robber and allowing them to skip town is expensive.