They do, and that is an option. I actually bought a GoPro this summer but ended up returning it, the issues being:
1. You have to buy a GoPro. Cheaper than a new ski, but more expensive than a $10 app. 🙂
2. The biggest issue is that the stabilization software that GoPro uses crops the sides of the video pretty significantly. This means in order for the skier to not go out of frame at each apex, you have to have the video zoomed out pretty far. This is even more pronounced at shorter lines. I had read that GoPro is too wide angle and always thought, "Whatever, I'll just zoom in while watching it back" but since the skier moves from the edge of the full frame to the opposite edge of the full frame, if you zoom in at any one point, the skier just goes out of the zoomed-in frame when they move side to side. I use video to watch myself back and critique my skiing, and the image was too zoomed out for that IMO, at least when viewing on the small screen of a phone.
3. There's the additional step of getting your videos off the GoPro and onto your phone or other device. You can send it via Bluetooth but it takes a long time or can error out, or you can pay for a GoPro cloud account and once you get home on Wifi it uploads, but that takes even longer, and when you access the videos within the cloud interface, you can only show max quality of 1080p. If you download the file to a device, you can get 4K, but that's yet another step of downloading off. You've also got to always carry the GoPro with you and make sure it's charged. Yes, none of these things is in itself a huge deal, but when I'm taking 12-18 videos multiple times a week, wanting to review them quick a couple times, maybe send one to a friend, and then delete them, the GoPro just added more work/inconvenience, opportunities for something to go wrong, etc. It's quite nice to just pop my phone on, which I always have and is always charged, and just have my videos waiting in my camera roll as soon as I'm done.
All in all, using the GoPro felt a lot less convenient than just using my phone, and while the image quality is good, the need to zoom out made even that not worth it. And if a phone app could actually capture in high-quality and be not super shaky, it's just as good as a GoPro and a lot more convenient!