When I was in high school, there was no double-bonus. It was 1-and-1 from 7 fouls on in a half.
The double-bonus takes a lot of pressure off someone going to the line and needing to convert the front end to remain ahead by more than 1 score. It also takes a lot of pressure off a coach who might otherwise decide not to play a poor FT shooter in favor of someone who can consistently knock down FTs.
With that stated, I'll stop my "Get off my lawn!" rant. I know this ship has sailed and it's never going back.
bonus rule benefits the more disciplined team that doesn't foul as much during the course of the half. If a team keeps their fouls down I think getting to force their opponent into three one and one's during crunch time is enough. I don't specifically remember the conversation about instituting the double bonus but I'm sure a big part of it was to keep trailing teams from starting to foul with too much time left turning the last couple minutes of games into a parade to the FT line.
...and I am OK with this exactly because of what you point out. However, making your FTs is part of being a good basketball player, and if the other team knew fouling the other team was unlikely to cut into the lead because everyone is a good FT shooter, they wouldn't be so inclined to hack away.
To add, I'm also OK with the 7/10 rule because without it, a team using the strategy to continue putting teams to the line for 1-and-1's extends the game, often times unnecessarily. Not only is it a parade to the FT line, but it's also a way to turn a 1.75-2 hour game into 2.5-2.75 hours.
Maybe someone knowledgeable on this can clarify if all states abide by NFHS rules.