No, this is not merely anti-AI sentiment or a complaint about how the AIs of today aren't really as good as they are being presented. For the purposes of this argument I'm assuming AIs will work exactly as advertised some point in the relatively near future and you really can just AI-prompt your way through a non-trivial problem.
The reason why we have way too much code isn't that code is too hard, it is that it is too easy. Modern cars are complicated, but their complication is restricted by the limitations of being in three-dimensional space, being something that has to be physically manufactured where each individual part is itself something that a person may have spent a person-month or three on, the failure rates of physical parts and how those rates multiply if you keep piling on the complexity, and so on and so forth. The result is that a car has tens of thousands of parts, but it can't have trillions of parts. It doesn't matter how many engineers you throw at the problem, nothing like a modern car could be that complicated. It would simply be guaranteed that too many parts would fail. (To be that complicated it would have to be a different kind of thing, like some sort of biological organism, which are themselves rather complicated. But we humans don't make those.)
We have monstrous code bases because they are easy to add to. We can add a new module and test that module in a degree of isolation no physical engineer could dream of. We have analysis tools with no physical equivalent. We don't even design the raw parts, which would be the compiled assembly, we have piles and piles of tools to take things much simpler to understand ("source code") and turn them into the final parts rather than working with the final parts directly. It is easy to be cynical about things like browser quality and I see a lot of fashionable poses struck about this on HN, but the reality is there is nothing like Chrome in the physical world. It is the software world whose artifacts are approaching biological levels of complexity. This isn't because we software engineers are special as people. Engineering tasks by their nature tend to rise to the maximum level of complexity the engineers can deal with, and we all have basically the same intellectual prowess. But we software engineers have unparalleled tools to deal with our complexity, so we get orders of magnitude farther down the path of creating it, and then having to deal with it.
Thus, when you understand that our code bases are complex because creating more code is easy, not because it is hard, you can then easily see that any paradigm shift that makes it even easier to create code means that we will have even more of it, not less. If I can type "Dear GPT-12, I don't like my web browser. Please write a standards-compliant web browser except the tabs stack in 3D in my VR environment instead.", and a few hours later the world actually has another 150 millions lines of code and a new browser (I'm assuming more standards the browser will have to implement in the meantime) to deal with, that's not going to contribute to simplifying the code world.
It will not be a situation where you "can" use AI tools. It will become a situation where you will have no ability to do anything else, and the code will naturally grow to the limits of what AI can deal with, until it then exceeds even those tools as much as our current code bases are exceeding ours.
Of course, then the question is, what will we get for that complexity? I don't know. But you'd better hope it doesn't break because your only option to fix it will basically be "Oh AI genie, please fix this code." And I do think I can guarantee a lot of quirkiness in the result, where things just randomly don't work and it becomes even beyond the AI's abilities to understand why.