Even on the dove cage, you're not driving the front of the preamp but the output stage. The line out and balanced out each use half of the 12AU7 and are controlled by the respective level controls. I had a dove cage/Minnie and I know what you mean about using the line level to push that 12AU7 stage but it's really more of a hack than a feature. It's so subtle (compared to different sensitivity settings) that I don't think it is missed at all on the integrated units.
Preferring the separate setup so you can do that is totally valid, but the 6SL7 preamp is where the majic happens, IMO, not the output stage.
Preferring the separate setup so you can do that is totally valid, but the 6SL7 preamp is where the majic happens, IMO, not the output stage.