Excellent thought provoking question about a scenario and a strategical decision that everyone will face, sometimes several times in a year.
I personally have never been one to foul in this situation. Not saying I would never foul in this situation. I just believe that fouling in this situation goes against my end of game coaching philosophy. One of the core values I try to instill in my player’s and teams is not to foul jump shooters late in the game and stop the clock with the lead. Plus of they make both free throws they can set their press up by a timely substitution. Not saying the strategy to foul here is wrong but I will take our chances with using an umbrella defense and make the opposition eat clock and make a very tough contested three pointer to tie and not bring in the opportunity to lose the game in this situation.
The worst that I see happening in this scenario if everything goes right for the opposition is getting tied up and going to over time. I just believe losing the game at this particular moment can not happen unless we open the door for them. Such as a four point play opportunity or send them the free throw line and they make one miss the second and tip the ball out off the rebound like Duke tries to do a lot to a three point shooter. I know you do not see this happen often but obviously it is a competitive game and now you are asking your kids to do something that is not normal under game pressure and that is foul with a lead and foul a non-shooter. The officials must agree they are a not in the act of shooting and it is a common foul not an intentional one as well. I am sure this can be practiced. Just like all of the end of game scenarios, like how to properly foul, up or down with time and score.
I will say that as a coach that this needs to be a predetermined decision before the game pressure is on. That way you make this decision without the game stress and are fully prepared to accept and defend your decision in this situation.