The dept. chair where I was adjunct--or was it the next office over?--had the office door plastered with bat child front pages (I could have sworn it was the more alliterative 'bat boy', but this one's non-binary for additional retrograde horror?).
This was a dept. where a professor also kept a large cane in his office--not that he needed it for locomotion, but because across the hall a professor brought in a large bodied, large toothed, small amiability dog. That also being equally across from my (now ex) wife's office, where my kid spent time when I needed to have him in day care, and where I spent time, my souvenir cricket bat also spent time. Cane, cricket bat, both good for swinging and dispelling large-toothed predators. (Sadly, when packing, my rubber-grip-bereft British-made souvenir striker was left behind, to protect the future denizens of said office.)
So, is a cricket bat boy to be understood as a [ cricket [ bat boy ] ] or a [ cricket-bat [ boy ]? Ah, my mathematical linguistics grad professor Ed would not like that, because they should mean the same. But cannot. Oh, noes. (Okay, okay, 2 different two-way changes in meanings, Ed; changing definitions mid-derivation is, um, not cricket. Continue to deservedly RIP.)