Unfortunately, I think you're right. My main issue is that I like the taste/texture with a paper filter but filtering a French press can be annoying. I wish I could have a machine hold the immersion chamber and dispense, but I think I just have to deal with standing there and slowly pouring the French press through paper.
Now that I think about it, last time I filtered the French press through paper without pressing it. Maybe I'll try pressing and then using paper 🤔. It's still not automated but it could at least cut my batches in half.