You don't need to get in shape for BJJ for the same reason you don't need to be in shape to start running or playing ping pong. Jiu-jitsu is a tremendously powerful tool to get in shape. The sparring and the drilling is really good cardio and burn a lot of calories as well.
A lot of people get in amazing shape just by doing jiu-jitsu. No pre-shaping is needed. That being said, we'd be lying if we said you're never going to be out of breath or gas out. But, funnily enough, that usually doesn't have much to do with your cardio/strength/bodyweight/ flexibility, etc. Especially not at the beginner's level.
A big part of grappling is making your movements as efficient as possible while forcing your opponent to waste as much energy as possible.
Over the years, we've seen marathon runners gas out during the first 2 minutes of a sparring round. They're efficient at running but not at rolling (yet).
The only reliable way to become efficient at jiu-jitsu is to train jiu-jitsu. So don't worry too much about your current shape and join us on the mats.
For more advanced competitors, being in shape does become more critical. Because they're dealing with similarly efficient people, any advantage in cardio/strength/flexibility/ explosiveness can give them the edge.
But if you're a beginner, don't worry too much about it.