I discovered this issue yesterday, and I see that the "fix" is that all component reorganization has to happen at the end of the timeline. That works fine, but it's a terrible workflow. It means that I can't ever clean up a project timeline.
In my case, I wanted to add in some subassemblies ("components") to my structure because I need to change the orientation of about 30 parts and I'd rather not do it individually. My original structure wasn't thought out too well (not uncommon when doing R&D design work), my timeline is fairly messy, and the whole file has become difficult to work with. I expected I'd be able to go "back in time" using the timeline and clean up the file to add more subassemblies, reduce the number of positioning and rigid group commands, etc., but since restructuring can only happen at the end of the timeline, I can't do this.
Since this assembly is going to continue to change several times through the R&D process I realized I can't continue with the current file, and I am now building an entirely new assembly file, and having to copy/paste new all the parts into a better thought out subassembly structure. This is time consuming and frustrating, especially since I expect I'll have to do this again on other designs. As the OP said, "I can't imagine ever knowing exactly the levels of nesting I'll need at the start of a design."
Please consider making the timeline an actual timeline, where you can truly go "back in time" and do anything at that point that you could do at the end of the timeline - I know it will break more stuff, but as long as I can work through those errors that's to be expected. Alternatively, it would be great if I could just redefine the owner of a particular component instead of needing a copy/paste timeline feature that gets put in at the end - in other words, let me roll back the timeline to the point of a component's creation, and let me drag it into a different part of the structure tree without creating a new timeline feature to show the move - have it act like I put it in the right folder when I created it. Sure this might break stuff downstream, but again, that can be dealt with.