Eventually money to invest will run out. If earnings of the companies doesn't catch up we'll reach a situation where stock prices reach a peak, have limited future expected returns, and then it'll pop when there's a better opportunity for the money

Imagine if interest rates go up and you can get 5% from a savings account. One big player pulls out cash triggering a minor drop in AI stocks. Panic sells happen trying to not be the last one out of the door, margin calls etc.

You're assuming cash will never stop flowing in driving up prices. It will. The only way it goes on forever is if the companies end up being wildly profitable