I have a few memorable Live Photos from family events; I like that feature.
I agree it could be cool, but also agree the implementation is poor. Firstly, the size will be an issue for some. If you are not computer literate then deleting the mov files could be a problem (I know a few that would struggle). Given how little memory is left out of a 16Gb phone (12.5 if you believe the phone and 10.5 if you believe itunes), it will be used in no time. I know people that have filled their 4s and 5s 16Gb phones due to apps and mainly photos..
Next it should be off by default for the above reason, and when first using the camera (or whenever it came out as a feature) it should have a message asking if you want it and warning that it will take up 3 times the memory of a normal photo.
The quality and frame rate is crap for the file size used.
And the phone should have the option of delete the mov files if not wanted. Chances are I'll never remember to turn it back on. If I could leave it on and then delete the unwanted mov files than that would work well. As said, 99% of the time only want static image as I use it as a work phone.