Of not there are the ones with three pedals, but sequential shifting. Like this for example.
That is just a different shift pattern and shifting mechanism on top of the GT3's traditional 6 speed gearbox. And in it's driving experience, operation and even internals it is more similar to a traditional H pattern manual than any of the automated 2 pedal transmissions. There is no robotized shifting or declutching, the driver has to do everything.
The bottom line is this - is there an actual mechanical link between the driver and the transmission or not? In the case of any of the different types of automated transmissions, the answer is NO. You request a gear change - ether by paddle, button, shifter, telepathy or whatever, it is really just an electrical signal that tells the ECU/TCU that the driver requested a gear change. It is up to the computer to then comply (if and when it wants) and operate the mechanicals that do the actual gear change. In the case of a manual, either one with a H pattern or a sequential pattern, both the clutch pedal and the shifter are mechanically linked to the drive line. And IMO it is this mechanical link that makes a manual more involving to drive.
I think this is also the reason (at least I) always perceive a small lag in the DCTs/automatics I have tried no matter how blindingly quick they shift. In the case of an automated transmission, the driver's part in a shift is done as soon as he/she requests a shift by depressing a button or pulling paddle. The real shift happens after the driver is done doing his part. Where as with a proper manual, the driver is only done when the gear change is done.
Interesting anecdote about this - I realized this when I was attending a tech talk by one of the Instagram founders. What they did to make their app
appear more responsive was while an image was uploading, instead of showing a spinner, they would ask people to fill out stuff about the image - description and crap. Their reasoning being human psychology is such that, people don't perceive time pass even if it ends up taking longer when they are actually involved in the process vs just ideally waiting.