Even an ancient pre-electronic planetary automatic can be built to shift faster than a human can row gears. Drag racing guys have been doing it forever, to the point that most performance car communities will have a "fastest <x>" and a "fastest manual <x>" if their vehicles were offered with both. Due to shift speed and a few other reasons it's just assumed that a properly set up automatic is going to be faster on the drag strip as long as the vehicle has enough power that the parasitic loss is negligible.
The responsiveness problem comes when you want a downshift and the transmission wasn't expecting it. It takes time to respond, even a DCT has delay in some cases, where a manual transmission is mechanically connected to the driver and thus has effectively zero lag other than whatever tolerances may exist in the various linkages.
I don’t think Ferrari even make manual gearboxes with clutches any more?
Haven't in like a decade.
For comparison, the dual clutch transmission in the Nissan GT-R can shift in 0.15 seconds and that's a 10+ year old car. The ZF 8HP, which is a conventional torque converter transmission used for example in the new BMW M5, is apparently able to do gear changes in about 0.2 seconds.
Sure, you can have an automatic that is incredibly slushy, but that's not an inherent quality to automatic transmissions.
Both DCTs and converter transmissions require far more maintenance than manual transmissions (e.g. DCT requires oil change every 60k, overhaul after 180k).
Changing gears on a manual transmission arguably takes more time, at least when the DCT has guessed correctly, but it doesn't matter nearly as much, because you, as the driver, are able to initiate the process in advance, because you have more information than the TCU, which approximately only has a tuple of (vehicle speed, engine RPM, current gear, gas pedal position, brake pedal position, D/S mode) to guess which gear to switch to soon.
Also, automatics still mean you have to know and understand gears, unless you live in a very flat piece of land, or don't care about fuel consumption and wear.
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.