While it only takes a few seconds to roll the newspaper to make the weapon, it does take time and attention to do so, so you're unlikely to be able to do it on the spot, in a crisis situation. Once rolled up, it has to either have constant pressure put on it to stay in shape, or needs to have some sort of fixative like tape used to keep it in shape, so the odds aren't great for preparing it in advance, pretending it's not a weapon, and then using it. Once assembled, it's basically just a stick, used for attacking in the same way as a stick. Ultimately, its intended use is for creating a sneak attack attack weapon in a situation where you've decided on a target, and have a few seconds to prepare to attack them.
If you plan on self-defense, you're better off just carrying a stick. You're probably not going to be able to fashion it after being attacked, and you're not going to be able to prepare it in advance in any way that maintains the property of not appearing to be a weapon while making it still suitable for use as a weapon. And if you are planning malice aforethought, other than the obligatory note that this is almost certainly illegal, and we advise you against it, you're still basically just beating someone with a stick, so afterwards, there will be the same sort of forensic evidence left behind, so the "concealed nature" of the weapon won't help you there.
The only case where I could maybe see this as a useful skill to learn for self defense, is if you're in a situation where you are under imminent threat, but have a bit of time to prepare to attack back, but even then, I suspect you'll find better weapons on-hand.
