Basically yes, you can install the app. Where is the data for that app stored? If on the phone, then your data is lost when your phone dies (maybe even when you switch phones). If in the cloud, that's great, but then someone else has your data. Selfhosting is to get the convenience of "the cloud" (multi-device/user sync and sharing) without actually relying on the cloud.

Take Jellyfin/Plex/Emby for example. Yes, you can just connect a laptop with and HDMI cable and play from VLC. Or you can just use an USB stick in the TV and play from the file system. But you have 2 TVs, a tablet, and a phone that all want to watch something from your movie collection. Of course you can just plug this stick into other devices, and use it that way. Or subscribe to Netflix that may or may not have the movie you want to watch. But what if you had your own Netflix that can be used by multiple phones, tvs and tablets, even at the same time? What if it even synced the progress of a series so your TV no.2 knows where you left off on phone no. 4? This is what self hosting is made for. You HOST "Netflix" yourSELF.