I have rarely evangelized trail braking, feeling that other skills are more important. I do see value in it however and do use it regularly. Everywhere? No.
When learning to ride, I think it's important to understand what control actions in a turn lead to getting the most stability and traction possible out of your particular bike. Bikes are more stable when the rider is slowly rolling on the gas than when s/he is off the gas. It's not a matter of setup. They are all that way. Some setups lead to being better off the gas than others, but it's still true the bike is more stable and offers its best traction with the throttle being rolled on.
Many people over the years have proven that to me convincingly. Onboard video and telemetry has proven it time and again. Personally, I prefer the bike to be in that condition for as much of the time as possible, so that's my default approach to setting up corners unless there are other, more important reasons to deviate from that approach.
That approach places demands on the rider. You have to be able to judge entry speed accurately. You have to be able to steer quickly, in the right location and by the right amount. Your throttle timing should be really good. Mistakes in these areas lead to going slower than you might want to (depending on your goal as a rider).
Keith Code wrote about trail braking before any schools were teaching it. He discussed it and taught it to riders in the early days. The CSS curriculum evolved to omit trail braking because many of the other skills seemed to require more attention and coaching to master. Riders were largely figuring out trail braking on their own.
In the meantime, trail braking has become very popular. While it's true the world's top racers use it, they do so in a framework where they have mastered other fundamental skills of going fast too. They know when the bike is in a condition that is best for it and they know sometimes they have to depart from that to the extent they can get away with to gain an advantage in certain situations. Riding schools don't all teach the same things. Sometimes it's as simple as a difference of opinion, sometimes it's because nobody else is addressing a particular aspect of riding and it becomes a market differentiatior. CSS has recently added trail braking back to the curriculum.
Trail braking has a lot of uses. One problem it solves very well is this: Riders who get all the braking done before turn entry frequently reach mid-turn feeling that they could have been going a little faster. When this happens, they may have set their entry speed accurately for their idea of what the target speed should be, but did not take into account that the bike will continue to slow past the turn point until the rider has cracked on the gas and rolled it on to the point where he is no longer slowing down. The rider who trail brakes tends to think naturally about mid-turn speed, knowing that his entry speed is higher than his mid-turn speed will be. It's part of his plan. I think most riders may find it easier to hit a desired mid-turn speed through trail braking than via a quick-flick turn entry.
Sooner or later, we will all need the brakes in a turn, no matter what our standard approach to cornering is. There will be deer. There will be sand. There will be blind decreasing radii. Riders who frequently use the brakes in a turn are equipped to deal with this in stride. Riders who have spent years believing it is a dangerous mistake to use the brakes in a corner may freak out. That is reason enough to become comfortable with braking in a turn. It's going to come up.
As much as I favor using the controls in agreement with what's best for the machine, sometimes it isn't best for the situation. A quick flick, constant radius line through turn 2 at Laguna is not the fast way through that turn. Sometimes preserving speed deep into a series of turns off a long straight is more important than creating ideal traction for the bike in that first turn. If one rider can pass another on the brakes at a turn entry, it may or may not be the fastest way, but once he's in front, he took the line. These are but a few examples of cases where an informed and skilled rider can decide what is most important in that situation.
As for a "standard" approach to cornering, I like to practice that which agrees with machine design and seems to require more maintenance from a skills perspective. On the street, that's usually a quick-flick approach. Just today, however, I took my son for a spirited ride up Redwood Road and found myself trail braking more than normal. I realized I didn't want to use the viscous quick flick I often use on roads like that with him hanging on for dear life, so I'd turn more slowly and control the attitude of the front suspension with brake pressure transitioning to cornering load. In that situation, it made for a nicer ride for him, while still being pretty entertaining.
