They cut out full pad practices to cut down on injuries. It's common sense.
Practicing more does not prevent players from getting injured. Nor does it make injuries less likely. The probablility would actually be higher. You can't practice how to not get hurt. Practice is for perfecting technique and implementing that weeks gameplan. Not going all out full pads during the week before a game. That's how you get hurt, if he needs conditioning; jump on the treadmill. These are pros, not high school. They get paid to play on Sundays, the rest of the week they need to be studying and light walkthroughs.
No you can't practice not getting hurt. You can, however, condition your body more to take the punishment of the game. If you don't practice then your body doesn't condition the same to that punishment as it does when you're practicing.
For example when you played high school, or even college ball, you saw a lot more people being dinged up with nagging injuries like hamstrings, or bruises and soreness in the muscles and over all body the first few days of practice, after having the spring and summer off. The longer you went along, into those practices and then into the season, you saw less and less of your team mates being dinged up by these injuries because their bodies had been conditioned to the punishment.
It's a lot like MMA. Those guys train on a regular basis, sparing and wrestling, to help condition their bodies to the punishment. Do you think they just walk in there, little physical practice as possible, and then just take hits like that? No.
You can't completely prevent injuries, there is simply no way, but you can help condition the body to the wear and tear of playing a violent sport and the only way to do so is practice in that violent sport. That's pretty well common sense to anyone whose played even 5 minutes of football in their lives.
That's why there is being in condition and being in football condition. They don't just say football condition just to say something cool and catchy.