Yes, there needs to be one somewhere in the system. Most catback intermediate pipes have them. Its the section right before the axle back. If you are referring to the uppipe, that is debatable. Some will say yes and no.
takes the stress from the movement of the engine/turbo from the welds and puts it on the flex, prolonging the life of the exhaust
^^^Exactly. Watch your engine when the car is started, or revved and you can see the engine torque under the force. Some of the twisting can be minimized by upgrading the rubber mounts to polyurethane, but its pretty expensive to do everything and it will make your car noisy.
I do not have any flex parts on my exhaust and I have never had a problem. I do have a 25 year warranty on my exhaust, so if a joint does end up breaking eventually, it is covered.