Yes, it's possible. It's also possible for experienced pilots to fly an airliner completely manually for the full duration of a transatlantic flight without crashing. Still, over the last decades, autopilots and other assistance systems with ever more sophisticated features have been developed, and I would argue that without this technology crashes would be much more frequent than they are today. Same goes for memory management: you can do it manually, and it might work out most of the time, but if the programming language is helping you with it, the likelihood of memory safety issues decreases drastically. And the problem with avoiding these issues only by "meeting certain standards of rigour" is that you might only find out that you have failed to meet them years later, when you learn that your software has a vulnerability.