For stationary pictures, as Opcom has explained, interlace does halve the bandwidth needed for a given resolution and refresh rate*. For moving pictures it's more complex. Yes, there is better temporal resolution for moving objects, though vertical resolution in those objects is reduced. Also when you try to de-interlace the picture, as required for LCD panels etc, you soon find out that it's not easy to do well.
It is now simple to do the TV equivalent of multiblade shutters as used in movie projectors. Framestores were a long way in the future in the 1930s
*It's not exactly half. There are additional artefacts caused by interlace that give a lower perceived vertical resolution than you might expect. The Kell factor is used to quantify this.