I've done Moai statutes before, it's not like I really evaluate things all that critically but the situation was prime for it, I settled that city with this plan already in mind and then the plan was to leverage the production to invade a neighbour so I had a short term goal in mind (not as though the invasion was entirely from the Moai hammers but it was early game and they helped). I thought it was successful and that city was very useful to me for the rest of the game because of it. I would consider doing it again.
Also Forbidden Palace might have situations going for it as well.
To answer Sampsa's related question. Yes I think an engineer WW rush can pay off. I've used a Pyramid GE to rush Hanging Gardens which when you add a forge at some point and run an engineer you can sort of get your original GE back and if you've just rushed and have heaps of cities the +1 pop can then be whipped to keep the war rolling. Sometimes the situation is that you don't have anything else profitable to do with it. Nobody to trade with / Good tech lead already / Bad engineer tech priority means bulbing isn't as good. Music GA coming so golden age not a great use. I can see the immediate boost of a Great Library, Great Lighthouse, Parthenon, Taj, Versailles, ...? being the best option in some situations.
But as I said, I'm no Wastin Time et al and I don't evaluate things all that critically, I just go with what feels right and that's probably why I get smashed on Deity.