The candela is based on Watts, but weighted to adjust for human perception. While the "standard human eye" could be considered a physical artifact, we use experimentally determined photopic (in bright light) and scotopic (in low light) response curves, which are supposedly fixed.

It isn't quite as fixed as some measurements since the average human's vision could continue to evolve and change the curve, or because we could find out that we measured it wrong, but it's not dependent on a single physical sample like the kilogram.