The reason to do this is basically visual. Sites looks nice, they have a "wow" factor and stands between other sites.
they're horrible UX.
We have tested this for our own site. People couldn't stop looking for the controls. They even reloaded the site thinking the transfer wasn't complete. A couple persons with a mild or borderline epileptic condition were clearly annoyed and all in all, it was a big failure (sadly, I loved it, see why you have to test?).
Basically, while there might be good reasons to use video backgrounds, you're also adding an attention grabber element that can't be dismissed and you're yelling to the user "hope you love this, because you have no control over it!"
There are some other resources studying this feature, the pros and cons (warning, not all is bad, it could be good in some cases, just TEST in yoru case).
See Background Videos - Good or Bad ? , Video Backgrounds : Yay or Nay for UX? , Tips For Designing With Video Backgrounds