One thing is for sure, video is IT! As the Boomers and the Gen Xers become much less of a driving force in the buying market, those in the know see a new trend in how the up-and-coming purchasers - the Millennials - are consuming online content. Those of us who have been in website design for a while used to design shorter pages, minimizing scrolling. We used images sliders, and (I shudder to even remember) flashing banners and Flash presentations.
However, Millennials consume differently. They don't care about scrolling (and almost all do it on phones), and they LOVE video, and it doesn't have to be a Spielberg epic production. Take some time to browse through YouTube and look at the content being uploaded. Or scroll (yes, scroll long!!) through Facebook and look at the plethora of "selfie" type videos. THIS is how Millennials are consuming content.
So, to answer the question in the title, "YES!" phone videos are OK to use on your website or blog. Millennials like the spontaneity of the "selfie" type videos, how they capture the moment. But there is a caveat here. While Millennials (and, for that matter, most everyone else) will accept that phone videos generally won't be in the running for "Best Movie" at the Emmy's, what they normally won't tolerate poor sound.
What does that mean for you as a website owner? If you're going to use phone captured video on your website, firstly make sure the video is in focus and isn't too shaky (check out the huge range of Gimbal sticks on Google or Amazon that are available). But the big thing is to make sure the sound is of good quality. The brain can fill in a lot of missing visual content, but cannot usually do the same for audio. If the sound is lost or muddy, we just find it annoying and frustrating. So, before deploying video content, make sure the audio track is understandable. Better still, have someone unrelated to the video review it. If we know what's being said, we CAN fill in the blanks, therefore we can believe the audio is OK. A non-biased hearer won't have that "heads-up" and will hear what others will hear.
The bottom line is that your website needs video - it's no longer a really cool thing to think about, it's a MUST HAVE! So, yes, phone videos are OK to use on your site, just watch the quality of the content. And ensure that the video is depicting what you need it to.
One last thing. Add your new video to YouTube and stream to your site from there. With Google owning YouTube this is a great way to boost organic SEO. You will also need to optimize you YouTube video too, but that's a topic for another blog post.