Marc, it is a very good idea to use a graphic as a background for the text filter. It is less effort than making and managing multiple images - especially since you “like to fade the text into the next clip.”
To get better fidelity using the image with burned-in text, you need to make sure the image is the same size as the project. If you are using Settings > Video Mode > Automatic, then the project resolution, aspect ratio, and frame rate are based on the first thing you add to the playlist or timeline - whichever comes first - and not the first clip in the project. In case that first thing is an image or audio file, it uses 1080p25.