Disc brakes certainly offer some advantages over mechanical rim brakes, but as a mechanical engineer, I disagree with your conclusions that the time and effort required to reach full braking force are less for hydraulics. Hydraulics don't respond instantaneously: even though hydraulic fluid is not (appreciably) compressible, the rubber seals in the pistons are compressible, and so are the brake lines. There is indeed a certain amount of "slack", for lack of a better word, to be taken up in the master cylinder as well as the disc brake caliper pistons before full pressure is reached. I'd say that "slack" is pretty comparable to the slack in a rim-brake cable system.

Furthermore, regarding the disc brake pads sitting closer to the disc than rim pads from the rims, note that the rim brakes don't need near as much mechanical advantage: the brake clamping force on a rim brake is sitting out on the rim, whereas the disc brake pads are operating very close to the wheel's axle. For a given stopping torque required, recall Torque= force times distance. Say the wheel needs 100 ft-lbs of torque to brake it to the desired braking torque, and the brake pads are sitting 1 foot from the center of the axle on a rim-braked bike; the brake pads require 100 lbs of clamping force (divided by the pad's coefficient of friction, let's assume it's a generous 1 to make the numbers even). But if the brake is a disc brake, and the disc is only 6 inches in diameter (3 inch radius), then the brake clamping force required would be 400 lbs (if the brake pad is the same theoretical coefficient of friction of 1). So the mechanical advantage of the disc system must be 4 times the MA of the rim brake system to get the same stopping torque. Now, even though the pad sits 0.5 mm from the brake rotor, the disc brake will move inward at 1/4 the speed (or distance) of a comparable rim brake system for the same brake lever "squeeze". In other words, if the mechanical advantage of the disc brake must be 4 times the MA of the rim brake, a 0.5 mm movement of disc brake pad would be equivalent to a 2 mm movement of the rim brake.

So by the time everything is taken into consideration, I'd realistically call it a wash as far as reaction time or lever effort for one system versus the other. The wheel needs a certain braking torque regardless of the brake system used, and the brake lever only has a given amount of distance available for travel inwards regardless of the brake system used--the same amount of work is available at the brake lever regardless of the system, no more or less.

Again, disc brakes have their advantages, as well as some disadvantages, so I'm not dismissing them; rather, just pointing out the real-world dynamics of the brake systems.