But you can anticipate the correct gear from the road, rather than having to wait for the transmission to respond to a call from the engine. Going into a curve, you can set a manual gearbox up before you get there so you have the torque to pull the car all the way around, rather than finding the car losing power halfway around.

The ideal combination would obviously be a manually triggered automatic (ideally dual clutch - the torque converter also adds to the mushy feel). But not like in my parents' B-class (a real old people's vehicle) with dual clutch, which takes what feels like over a second to respond to manual inputs. Shifting back a few gears (out of seven) for engine braking is an exercise in frustration.

You can manually select gears on automatics you know.

In most, not so quickly - plus you can't slip the clutch across the transition across gears.

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.

The problem with e.g. DCTs is that it can't do 0.x seconds consistently. It can only do that if they are switching from an odd to an even gear or vice versa where the target gear has been pre-selected. If the wrong target gear is pre-selected, it takes 1.x seconds. There are extra delays from where you'd want the gear to be engaged to the TCU noticing that it needs to be engaged to the gear actually being engaged. The former delays were quite dominant, esp. in older implementations (I don't know how much progress has been made).

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.

It's not about outright speed of shifting, it's about the feel. While a DCT or automatic may boast better performance numbers, they are not nearly as satisfying as a well-balanced clutch and nice mechanical shifter. It just feels better to wring out the engine and nail the shifts than it does to pull on paddles.

OP didn't mention other types of gearboxes like DSGs. They have their advantages and disadvantages too and are only available on a limited number of vehicles.