The stills captured in video are significantly lower quality than the still image at the heart of a live photo. The few frames of captured video and audio are to provide "live" context, not to let you choose the best shot. It was never intended as a burst capture tool, the iPhone has a separate burst mode by holding down the shutter button that works sort of how you are describing, and will provide a rapid burst of much higher quality stills.
You can change the keyframe on a live photo (ie the image displayed first) from the still capture to a video frame, but I generally would never do this due to the quality drop. It adds a little more memory context to a still photo, its not a burst capture tool.
There are actually some features with live photos I hadn't seen before though that are kind of interesting, for example you can fake a long exposure shot via a feature that interpolates information from the video stills into the main image:
https://osxdaily.com/2018/01/10/take-long-exposure-photos-ip...