Seems like it makes the problem worse because you are then tied to a specific version at time of publishing and need to republish to get any framework patches.
Indeed. Microsoft identified this as a problem as well and pushes .NET security patches via Windows Update nowadays. When using self-contained apps, you won't get these patches.
You missed how there effectively isn't a .NET Core/.NET Framework delination anymore. It is just .NET, and .NET gets security patches from Windows Update.