It's pretty simple to see that traditional braking triggers brake lights, while engine braking does not. Brake lights are there for safely, to prevent rear-ends. I'd be shocked if any driving education program encouraged engine braking.
On a slightly different note, if your rev-matching isn't smooth when you downshift to engine brake, you're just using your clutch to slow the car, which is a much more expensive part to replace than brake pads/rotors.
In most cases when it is appropriate to use engine braking the person behind you has to already start matching your speed. In situations where you have to brake suddenly and quickly brake lights can warn the other driver, but in most cases when you are downshifting to engine brake you are slowing down slowly enough that the person behind you can make proper adjustments simply based upon the fact that they are now getting closer to you. It's a human PID loop!
As for rev matching, yes, completely agreed, if you can't rev match your down shifts then engine braking is indeed going to use your clutch and that is more expensive to replace. However, if you are driving a stick shift car and you don't know how to properly rev-match on downshifts how will you easily get up the mountain where shifting from fifth to fourth to third is sometimes required simply to keep up with traffic properly? I can go from fifth at 3k to fourth at 5k without issues. Rev-matching in a stick shift is very important outside of the engine braking use case.
During my driving course they always told me to apply the brakes, if only very lightly, while downshifting. This way the brake lights are there to warn people behind you. I always do it (even on motorbikes with the rear brake). I thought it was pretty standard.
It's standard dogma, including in the advanced driving courses (eg. police). "Gears for go, brakes for slow"
Why this is so, I'm not entirely sure; it does mean that you can change from manual to auto transmission without thinking (and potentially without making a fatal mistake at speed if you are pursuing a suspect). However, it just shifts the cognitive effort of making sure you're always in the correct gear (which I think is also standard advice in eg. the roadcraft system).
From a professional owner / driver perspective (eg. a taxi), the answer is simple; brakes are cheap to replace, clutches aren't.
What they really don't tell you about are things like left foot braking (which I don't do) and heel-and-toe (which I do, especially when leaving motorways where we tend to have a junction followed by an uphill slip road).
Moving from an manual to an automatic can still be quite jarring, even if you don't have engine braking. Ever been in an automatic after driving a stick shift for years? The brake pedal is twice as wide and is in approximately the same location as where the clutch is found ... get into an emergency situation? Your mind will automatically want to disengage the clutch and hit the brakes, so you go for where the clutch pedal would be normally and instead hit the brake pedal ...
Yeah, I was used to driving my Subaru Impreza with a stick shift, then I drove my dads BMW 5-series, got into a sticky situation in traffic and had to come to a quick and sudden stop, there was no thinking involved, push the clutch and the brake was my immediate reaction... let me tell you, that BMW stopped on a dime, luckily there was no-one behind me or I'd have to explain to my dad how instinct and sheer muscle memory on my part caused someone to rear-end me and ruin his car, all because my left foot went for the clutch and caught the edge of the brake pedal...
Some automatic cars even put the parking brake on a pedal close to where the clutch is on manual. It's quite... surprising when you're used to drive stick.
On a slightly different note, if your rev-matching isn't smooth when you downshift to engine brake, you're just using your clutch to slow the car, which is a much more expensive part to replace than brake pads/rotors.