Hi sleeptowin.
As you'll have gathered, no-one knows the answer but my theory is that it wasn't the only one but all the others were wood and rotted away.

If you look at the lintels you'll see they each have 2 different classic carpentry joints in 4 different positions, AND they're curved. Ideal for a small wooden structure with tight joints but a bit mad for huge and very hard stones. Also, a pointless design because unlike in wood there was no way the joints could be made tight fitting or have dowels inserted. It looks like a show-off piece rather than a well-designed one.