If I owned a carpentry company, and I was trying to hire a carpenter, yes, I would ask them to build me something. Maybe not a dog house, but a bird house. You don't think that would be reasonable? "If you want us to hire you as a carpenter, prove to us you can build a bird house first." That seems totally reasonable to me.

If I hire them to fix my roof and they leave a huge hole in it, I am expected to sue them and wait for a few years to recoup my losses (while having a huge hole in the roof).

I think I prefer the coding test.