The I-frame encoding in MPEG-1 was basically identical to baseline JPEG. The compressed frames can be losslessly converted to JPEG and vice-versa. So, in a sense, we were already there.
Reusing the I-frame compression from a video codec is the only strategy that makes sense for a lossy still image codec. Video codecs are where the major innovation is happening, with wide participation from every player in the industry, and a large part of the innovation has been around improving I-frame efficiency. They're being hardware optimized and baked into software implementations. And even when patents are involved, still image codecs are usually able to piggyback on the video codec licenses that are already on the device.