"Live Photos" and "Motion Photos" are videos with additional post processing to align frames and eliminate movement in areas of the scene that show minimal changes. They are not single frames selected from a video or burst of frames.
Most modern cameras, including DSLRs, do include the ability to capture video, but have not been programmed to perform the post processing to produce the results you desire. Smart phones can produce them because they are general-purpose computers which can easily be loaded with new apps and updates.
In principle, a camera could be programmed to produce Live/Motion Photos, but the amount of time it takes to post process in camera would be intolerable to most photographers, who would normally prefer to spend the time and battery power taking more photos. However, my camera does include over a dozen ludicrous toy camera effects. Live/Motion Photos could easily be added to the list if they become popular enough.
When people have their attention divided among too many tasks, results are usually subpar. You will get best results by hiring people who are specialized at producing the specific types of output you desire. If you want still photos, get a photographer. If you want video, get a videographer. If you want Live/Motion photos, get someone to produce specifically those.