It all depends. Yes, something like that happened with Uber, but computers and consumer electronics have Moore's law working for them, so prices usually go down. (With occasional shortages like we see now with RAM - not for the first time, but it's usually temporary.)

My guess is that AI will be more like consumer electronics than like Uber.

I agree that consumer goods normally get cheaper over time. Software that becomes commercialized, or sees a surge in enterprise demand, tends to go the other way. Splunk, Elasticsearch, and Slack for example.