The property you're talking about (next bit unpredictability) is important for a CSPRNG, but it doesn't matter at all for a PRNG. A PRNG just needs to be fast and have a uniform output. LCGs, for instance, do not have next bit unpredictability and are a perfectly fine class of PRNG.
The paper that triggered this thread "breaking" PCG sees it as potentially in the same class of issues as using RANDU.
> our results […] do mean that [PCG']s output has detectable properties. Whether these properties may affect the result of Monte-Carlo numerical simulations is another matter entirely.
Again this is on PCG which required a breaking effort.
The short version of Xorshift as originally presented by Marsaglia outputting its whole state for example is bound to have behaviors like my room-generation example emerging fairly easily. Particularly, with low hamming-weight states.
I doubt Xoshiro's output is that bad but if presented as trivial to recover vs PCG, that to me indicates potential issues when using the output for simulation.
