In your view? Reproducibility is essential to scientific progress because it defines what science is. It's the backbone of science. Hypothesis,testing/experiments. It's what separates science from math, arts and pseudosciences like social "sciences".
> I'm sure if you went back through the literature on something like electromagnetism, you would find results that fail to replicate, yet the theory of electromagnetism if applied properly is remarkably robust.
How would it be "robust" if it couldn't be replicated? How would the theory of electromagnetism be robust if it failed to produce replicable results?
> Scientific results can be strengthened by replication
No. It can only be a "scientific result" if it can be replicated/tested. It's definitional.
> Discovery of a psychological "effect" is perfectly scientific and interesting
No it isn't if it can't be test/replicated/reproduced. It's not science. It's something else altogether.
> And if those sciences are also plagued by irreproducibility, then they may embrace scientific methodology without producing a useful scientific knowledge base.
There is no "scientific methodology" without testability/replication/reproducibility.
All science is based on hypothesis-testing.