Yes and no,

Interlacing isn't exactly half the frame rate or resolution.

Interlacing is a tie over from Cathode Ray Tube televisions. Back in the early days of television, an electron beam would excite phosphors on a screen to produce an image. The problem was that the phosphors would start to fade before the beam could excite the whole image. This resulted in a slow black band moving up the screen. To solve this they split the image into an odd and even field. This was faster to scan and meant that the cathode ray could keep up.

Most people assume that an interlaced image since it is displaying half the resolution is equal to either half the frame rate or half the resolution, but this isn't strictly correct. It still records the same number of lines but it does them in a batch of odd or even, and is still records as the same frame rate (in this case 60fps) it just does half and then half that is 120 half frames a second. Also it doesn't use the same lines each half frame but does in fact use the full area of the sensor

This is where it gets confusing but basically a 1080i sensor still has 1080 lines of resolution and it scans them 60 times a second, it just splits this information up into 120 half chunks.

For a digital device this is more about processor speed and bandwidth. an interlaced signal is easier for the device to process than a progressive signal as it can deal with the data in smaller chunks. Also whilst it is theoretically possible to use a 30p sensor to produce a 60i signal, the image would appear distorted as there is a line shift between the odd and even lines on the sensor that would make the image look unnatural and movement appear a little stuttered.

So in short a higher fps interlaced signal is still better than a lower fps progressive signal, but obviously a progressive signal is better than its equivalent interlaced signal.