I did professional waterfall development and SDD is exactly waterfall. The problem with waterfall was never the time that it took, it is that the spec locks you into a small niche and iterative changes force enormous complexity to keep spec and code consistent.

The problems with waterfall come when much of the project is done and then you discover that your spec doesn't quite work, but the changes to your spec require half the requirements to subtly change, so that it can work at all. But then these subtle changes need to be reflected in code everywhere. Do this a couple of times (with LLM and without) and now your code and spec only superficially look like one another.