I agree a fluted spike would be nice, but I think that this helmet may be the exception for several reasons. First, this is the cleanest, most un messed with helmet. Second, the helmet is huge. I have a large (60 cm) head and it fits me fine. This leads me to think the officer may have been unusually tall. If one was so tall, he may need a special helmet that deemphasizes his height and avoids the embarrassment of striking his spike on low doorways and chandeliers. Third I tried a fluted spike on the helmet and it threads OK, but doesn't seat properly, the round spike seats perfectly. This is because although the cruciform base plate looks in every way Bavarian, with 6 holes in the throat, the top portion, however, looks like a Prussian helmet where the spike meets the base. The spike is also a officer spike and is the shortest one in my collection, no advantage to replacing a spike with one of equal value. Fluted spikes are typically on the long to very long side.
Here are some pictures for comparison.