The 1 and 1 rule puts a premium on several things (and not having it takes that premium away).
There is the obvious free throw shooting ability for a team and individual players.
Then there is the ability to shoot in the clutch while KNOWING if you don't hit it you don't get a second attempt, which adds pressure to the first attempt.
Strategy changes. As I already said, hacking becomes MUCH more effective against a player like Shaq because you not only have a bad shooter there but you now have a GREAT chance of coming away without the other team scoring at all (if he misses, assuming you can get the rebound).
Both sides of the ball are affected: How long do you leave the Shaq-like guy on the floor? How soon do you start hacking? How far behind do you need to be, or do you need to be behind at all (i.e. if the guy is that terrible, do you start hacking him near the end of the game every time even if you're tied or in the lead knowing you can get a zero point possession as a reward)? How much more do you put the really good free throw shooters on your team (and on the floor) even if they aren't the best overall player you can get there?
I've always thought free throw shooting is under used in many basketball games, including the NBA (as we discussed here) and even pickup basketball, where it is largely neglected for shooting fouls for no real reason This is why I won't play pickup games most times - if you hit me when I"m shooting, you should pay to the tune of my 92+% ability to hit from the charity stripe, not get to keep fouling me every time I go to shoot because there are no free throws.