Actually it's non-moving shots that interlacing helps. For a given bit rate, you have a certain amount of resolution you can represent. On progressive scan you have to show every line in the same frame, so there's less information you can squeeze into that bit rate. If you instead skip every other line for one frame and do them on the next, and back and forth, you can represent the same resolution at half the bit rate. However, when your footage is in motion, there will be scan lines on the edges of the motion as you are combining two different frames where the subject was in two different places.
That's an ugly artifact and for fast-motion shots you would often rather do 720p than 1080i. But for still shots with no changes from frame to frame 1080i is essentially just as good as 1080p yet half the bandwidth, and for the same e.g. 50Mbps bandwidth the 1080i will actually be better than what you can do 1080p at least with an intraframe codec. Long GOP codecs like H.264 relieve a lot of that problem by incorporating information from multiple frames, but introduce other artifacts of their own.
You can interpolate 1080i60 to 1080p60 for slo-mo but you do run the risk of the interlacing artifacts on edges. This is how you can get slo-mo on the C100 for instance. All the 4K modes for the BMD listed are progressive and therefore can't be used for slo-mo other than with something like Twixtor if that supports 4K now.