All of this is my opinion and I how I talked myself through switching from how I was driving/riding to how I do today which admittedly is not biased towards aggressive riding. These days I would rather focus on being quick/smooth/safe.
Having recently switched to trail braking (in the last half dozen years) I can say that it is a much more effective way for me to get through a corner. I was the downshift, engine at high RPM, ready to drive out of the corner, working to balance the engine, brakes, clutch guy (car or motorcycle). When I stopped to think about it (after watching numerous onboard cameras of fast riders and drivers) I started looking into why I wasn't hearing the same thing from those videos that I hear from my riding/driving. Eventually it came down to watching in car videos and stumbling on trail braking online. Also a track-side comment to me from a fast driver along the lines of 'man you beat the snot out of that motor' helped me get some clarity.
Braking; Brakes are cheap, engines are not. All of the maintenance I will ever do by swapping the brake pads out every couple of years will not add up to the cost ($$ and time) not to mention temporary loss of confidence in my machine if I have to do an engine swap. Engine braking is unpredictable, the only inputs you have are gear, and clutch. Pick the wrong gear and it doesn't work they way you *need* it to, and using the clutch to disengage braking forces or change gears is ultimately a bad idea and one more control than you really need or want.
Using brakes only allows you to focus on one less set of forces, the remainder are tire rotational speed, bike attitude, and brake balance. If you think about it, you want to be on the front brake as much as possible without losing traction, thank you linked braking for making this even easier. Not only will it reduce your corner radius faster, it should simply be more predictable. When you use any brakes the bike will naturally shift its balance forward, biasing too much on the back brake robs you of critical input, that being when the front is going to wash out but more importantly, you want the transition from braking to cornering to acceleration to be as smooth as possible. Using the front brake allows you to control bike attitude and provides you with direct feedback/control of front end traction.
Cornering; 'Settling into the corner' ... You want the bikes suspension to compress and stay in a small range of attitude (position in 3D) throughout the corner. This will allow the suspension to work efficiently and you will be smoother in the corner. Using the front brake and throttle to drive the corner will provide you more focus as the brake becomes the overriding concern. The front brake is about controlling the bikes attitude in the corner, as you increase brake it wants to turn in as I release brake the bike wants to stand up. The right combination will be one that has the bike doing the right thing at the right time. Trail braking is brake releasing in my mind. It is the act of not letting off the brake completely until the corner requires it, already being into the brakes with the bike settled also allows for quicker, smoother reactions if something goes wrong.
Acceleration; Ideally in your drive out of the corner you are in the highest gear that will allow you to use the most appropriate part of the torque curve, typically this will be right under 5K rpm, for me around 4200. To be smooth out of the corner your job is to apply power without losing traction, this does not mean being at peak torque, at least for me. I found that it is more useful to 'torque' my way out of the corner and build towards peak power. Some guys who are faster can probably get away with tightening this up (by being in a lower gear) but for me it is more enjoyable, smoother, and ultimately safer to build build speed by leaning on the bikes torque curve.. which means being a gear up in many cases as I would rather be in too high of a gear than too low. These are public roads after all and there are real concerns about dust/gravel/tar snakes/road patches and the general fact that the road maintenance crews are not concerned with your corner traction. Building power/speed smoothly goes a long ways towards offsetting some of these surprise issues.
Anyways..engine braking is not the solution (for me)..