Nowadays more and more sites are joining the trend of having a muted video being played in their landing pages. In fact, I'm also working in a fitness app and we've recently redesigned our landing to be on the cool side(?
Jokes aside. I know this case is different, but a big video of good quality just surprising you and welcoming you into the site can be stunning.
I don't know much about splash screens but there are many examples on the web of landing pages with videos, like airbnb and netflix some time ago.
That being said, a big problem that someone has pointed out at me lately is that if you don't choose the video images carefully, and it's colors are very similar to the colors of the text (if you happen to have text above the video images, like a 'welcome' text or a navabar at the top) they can easily blend together making reading a little bit difficult.
So maybe this could be a reason of why someone wouldn't want a video playing on a splash screen, especially if there is a lot of text to be displayed, but at this point I'm just speculating. All the other things @Aidan said seem reasonable too.
If you decide to keep it, just remember to pick the right pictures to make the experience effortless and friendly.