Just to get you back in the conversation Lol
I think in general what you are saying is true, that in a lot of crashes, HOW the front brake was applied is a huge part of the problem. In the case of the OP's crashes though, because of the low speed and the fact that he is applying the front brake while turning the bars drastically- that is HIS problem. I'm short, only 5"3 so I have to be particularly careful whenever stopping or slow speed manuvering the bike because I only have tippy toes that barely touch the ground. If I place my foot wrong or have the bars turned too much with some front brake on and the bike starts tipping, I'm going down.It's not front-wheel locking that's problem, it's how it's applied. Most beginners panic, grab both-brakes as hard as they can and end up locking both. Proper procedure is to apply both and gradually increase force. Then as rear lifts due to weight-transfer, let up on rear (or leave it locked as trained in beginner crashes).
In vast majority of crashes where auto cuts in front of rider's path, there's LONG skid-mark of rear locked-up tyre leading right into crash! If they had properly used front-brake only, they would've stopped in plenty of time.
Imagine an invisible-hand pushing back on bike to decelerate. This braking-force is applied at tyre's contact patches. Due to C.o.G. of bike+rider system being higher than this force, weight-transfer towards front due to deceleration causes weight-transfer to front and tipping up of bike around front contact-patch.
The higher the deceleration-force (Bf), the higher the weight-transfer. Maximum amount of braking-force is when 100% of weight is on front-tyre. This is when front-tyre has highest friction f=mu. Similar to wings on F1 cars pressing more on tyres to increase traction. If Bf was lower to put rear-wheel back on ground, deceleration would be less.
Reducing braking-force in this case would have him miss turn and go off-road. Note no back brake used at all.
Even 12-yr old girl can do it!
The solution is improved braking-technique through lots of practice.