Using video on your homepage makes sense when it serves to improve user experience, UX.
When creating content for your site, you want to have content that will engage different types of people. If someone is searching specifically for video about your product or service, you’ll want your homepage to show up in those search results. Adding video to your homepage will accomplish that.
You need to decide where to place the video on the page. A still of the video could serve dual purpose as the primary image for the page.
Consider if you want the video to autoplay, or if you want your visitor to choose to play the video. If you know that your target audience views autoplay in a negative light, like a popup, then that might not be the way to go. Depending on what you say in the video might determine if autoplay will work. If the video introduces the site, tells them what else to engage with on the homepage, it may work well.
Just remember to keep everything above the fold, with the video on one side and your anchor text and CTA on the other side.