You're confusing speed with latency. The feeling of "responsiveness" leans a lot harder on the latter than the former.
Even traditional hydraulic planetary automatics, the ones associated with the term "slushbox", have been able to physically change gears faster than most humans could row a manual for a long time. They have a similar advantage to DCTs in that gear changes are just a matter of applying and releasing different clutches, so they can on paper be in the same ballpark at least as far as WOT upshifts go.
The biggest problem manual enthusiasts typically have with automatics has been the downshifts. Most obviously the old-school automatics that had no idea when you might need a downshift until the driver pushes the pedal down harder, but even the more modern ones with "manual" modes. For the most part these are just asking the transmission controller nicely to change gears when it has a moment. The actual gear change itself may take place faster than I could move a stick, but the amount of time between me deciding I want to change gear and the gear actually changing goes in the other direction. Sometimes it won't even let me downshift to a valid gear, many automatics in less sport-inclined vehicles won't downshift unless the engine would still be under 4500 RPM even if they redline north of 6000.
A good DCT is almost there. They still struggle with multi-gear downshifts so a tight corner off a high speed stretch is uncomfortable, but as long as you're going one gear at a time they work great.
Even traditional hydraulic planetary automatics, the ones associated with the term "slushbox", have been able to physically change gears faster than most humans could row a manual for a long time. They have a similar advantage to DCTs in that gear changes are just a matter of applying and releasing different clutches, so they can on paper be in the same ballpark at least as far as WOT upshifts go.
The biggest problem manual enthusiasts typically have with automatics has been the downshifts. Most obviously the old-school automatics that had no idea when you might need a downshift until the driver pushes the pedal down harder, but even the more modern ones with "manual" modes. For the most part these are just asking the transmission controller nicely to change gears when it has a moment. The actual gear change itself may take place faster than I could move a stick, but the amount of time between me deciding I want to change gear and the gear actually changing goes in the other direction. Sometimes it won't even let me downshift to a valid gear, many automatics in less sport-inclined vehicles won't downshift unless the engine would still be under 4500 RPM even if they redline north of 6000.
A good DCT is almost there. They still struggle with multi-gear downshifts so a tight corner off a high speed stretch is uncomfortable, but as long as you're going one gear at a time they work great.