The "8 additional spatial information" is not necessarily a good thing, because LW is an average. Just like frequency response smoothing can be misleading, spatial averaging can be misleading too. In particular, it can make variations at individual angles appear smaller than they really are.
Consider this: there could very well be frequency response anomalies that shift in frequency depending on angle, because they are related to the difference in distance between speaker elements (e.g. interference, diffraction). That's a real problem that could be audible, just not always at the same frequencies depending on what specific angle you happen to listen at right now. But because of the way the averaging works, if you take the average of multiple angles where the anomalies are not aligned in frequency, you might get a response that looks much flatter than any actual response you can get at any angle.
That's not to say that the opposite, that LW is meaningless, is true, of course. LW is useful because it can tell you if some feature at a given frequency in the on-axis response is specific to the 0° angle or if it persists over small angles as well, which is useful information especially if you want to determine what kind of anomaly you are looking at (resonance, interference, diffraction, etc.). That's why the standard spinorama includes both on-axis and LW; one is not "better" than the other, they serve different purposes and it's really the combination of the two that's most useful, not one in isolation.