Why do some camcorders record in 1080i?
It uses a lower data rate (within the TV, not for the actual signal) and is cheaper to produce.  That is all.  The only difference is that if you are going to view it on a 1080i display, then shooting in 1080i would look slightly smoother since half the information updates every half a frame rather than updating the whole thing at once, but 1080p is preferable pretty much hands down on a 1080p display.

Interlacing just means that the upper and then lower fields update alternately.  It's less difficult to fake interlacing than it is to deinterlace, but you still get some artifacts displaying a progressive scan image on an interlaced display because of how things update.