All we can tell from singularities is that GR might have a realm of applicability ... like every other theory ever. Not that its wrong.

"Has a realm of applicability" is what people mean by "wrong" here. As in, the equations we have don't fully generalize and explain all regimes. The "right" model will cover all regimes and still reduce to match what we already have.

Then every physical (and nature) law is wrong. Only math is right. There's not a single law that covers full regime for at least one definition of "full".

Possibly, but we're converging on something correct as we cover more regimes in this inductive process called science. That's the best we can do.