As a side note, this might just be a me thing, but I distinguish between "complex" and "complicated". Certain things have an inherently complexity. Stripped to their essence, they're still going to have a lot of moving parts. It's just their nature. However, you can also add complication on top of something that makes it more complex than it needs to be to perform its function. Think "complication" in the watchmaker's sense. It might be neat to add a dial that shows the number of weeks since your last dentist appointment, but you don't really need that to have a functional wristwatch, and its presence makes the whole thing a lot more finicky and fragile than it would otherwise be.
Complexity is fine. Sometimes we're working on complex problems without simple, straightforward, correct solutions. I do try to avoid complications, though.