Fair question, and honestly nothing stops you. You can absolutely wire a bubble to a YouTube embed. But that afternoon project turns into something bigger fast.
YouTube fights you on this. Embeds pull in the player chrome, "related videos," cookie banners, and they resist muted autoplay especially on mobile. You wanted a clean talking bubble and you end up with a mini YouTube that has their branding stamped on your video.
The invisible part is where the real work is. Recording in the browser, background blur, masking it to a circle, transcoding to both webm and mp4 so it plays everywhere, poster frames, CDN hosting. YouTube hides all of that and owns it. The whole point is that you own it instead.
Then there's the product side. Which pages it shows on, when it triggers (on load, on scroll, exit intent), how often the same person sees it, and stats on displays vs actual plays vs clicks. That's the difference between a video floating on your site and a tool you can actually measure.
So you're not paying for some un-copyable magic. You're paying to not build or maintain any of it, and to have it just work on day one. If building it yourself sounds fun then genuinely go do it, you'll learn a lot. The SaaS is just for people who'd rather ship it in five minutes and get back to running their business.