Complex systems fail due to single causes exactly that way. First the system runs well; once the cause is introduced the system adapts so that the visible cost is minimal, but the adaptations are costly by themselves, and demand further adaptations; then the adaptation cycle runs for a while (that can be very long), until everything finally breaks down.
It is very unlikely that the lead pipes that were there since the beginning would be such a cause, but the duration of the fall alone is not enough evidence that it wasn't caused by an immediate problem.
You can use a caustic solution to unclog your pipes and it will work flawlessly, every time for an indefinite amount of time. Then, at some point, you'll have leaks due to glue being eaten away, PVC melting, or other damage.
True for complex systems, but West Roman empire didn't "collapse" instantaneously, nor within a year/decade.
If I remember correctly what I read on it, the actual date is arbitrarily taken for didactic clarity, and it's the date the capital moved to another city. But the kingdom still called itself Roman, so contemporaries didn't quite notice the difference. BTW, this is how modern Romania got its name -- smaller kingdoms in the former empire called themselves the glorious Rome.
The curious detail is that Barbarian leaders actually wanted to become king of Rome and to be acknowledged as equally civilized, rather than merely sack and loot it. Some of them were actually legioneers, if I remember it correctly. So it's not clear if a legioneer sacked Rome and set himself as king, was the new state still Roman or already not.
Tainter deals directly with the Roman Empire, but the nutshell is the cost of complexity begins to outweigh its returns, requiring more and more resources just to maintain the status quo, until the entire thing becomes weak and susceptible to failures large and small.
- "Panarchy: Understanding Human and Natural Systems" (Amazon link: https://www.amazon.com/Panarchy-Understanding-Transformation...) is also a fantastic book drawing from ecosystem science and proposes a general model for this. It's pretty well accepted in ecological circles but has been criticised for a lack of empirical data. The general model is the same as Tainter's though.
It is very unlikely that the lead pipes that were there since the beginning would be such a cause, but the duration of the fall alone is not enough evidence that it wasn't caused by an immediate problem.