You don't need to. But it will allow you to press more weight with less risk of injury. It only feels unnatural because you're used to just lying flat on the bench with a relaxed back - doing that now feels "unnatural" to me.

Try this: walk over to a nearby wall and "try" to push it over. That is, put yourself into the position that feels like you have the best brace and power to transfer force into the wall, and actually do it. Notice where your hands, elbows and shoulder blades end up. That's basically the same position as a good powerlifting bench.