My jury is still out as to whether the current models are proto-AI. Obviously an incredible innovation. I'm just not certain they have the potential to go the whole way.
As you say, whether we call it "AI", or "doohickey", it is an incredible innovation. And I don't think that anyone is claiming at the moment that the systems as-is will themselves "go the whole way" - it is a technological advancement, that like all others should inspire practitioners to develop better future systems, that adapt some aspects of it.
Perhaps at some point we will see a self-propelling technological singularity with the AI developing its own successor autonomously, but that's clearly not the current situation.
That will never happen. We may approach that state asymptotically but since AI output is stochastic, and humans' goals change over time, humans will always be part of the loop.
Whatever the formula for the probability of recursive self-improvement of AI may be, I am unfortunately certain that the fickleness of human goals does not factor into it.
I'm a booster, but LLMs are 100% not going to give us true autonomous intelligence, they're incredibly powerful but all the intelligence they display is "hacked," generalization is limited. That being said, people are making a huge mistake with the idea that just because we're not gonna hit AGI in the next few years, that these tools aren't powerful enough to irreversibly transform the the world. They absolutely are, and there's no going back.
Conclusion: we are not in the age of AI.