Somehow the threads about solo diving or self-reliant diving turn into a discussion about the acceptability of it, or a breach of the buddy system. But there are many situations where self-reliant diving is a must.
The most common situation: an instructor taking novices into the water for the very first time. If anything were to happen, the instructor cannot rely on the buddy system, as the novice divers in his/her group are likely completely unaware of any problems. Everything is completely new, there is no experience that tells them what is out of the ordinary. The instructor is effectively diving solo.
A less common situation, but one that is hardly ever given much thought:
Dad goes for a dive on the housereef with his 11 year old daughter. They're both certified, they've both learned how to share air in case of problems.
But in real life, the 11 year old kid is not gonna save her dad in case the water turns brown. You can't expect the same reaction from a child in problem situations as you can expect from an adult. In such a case where an adult takes a kid diving, the adult should be very aware of this situation and realise that (s)he is effectively diving solo. Being self-reliant certainly has added value.
Technical diving is a different story, since it's based on self-reliant divers in a team. It's however beyond the realm of recreational diving, and you can't expect the knowledge about technical diving to be present in a recreational divecenter. However the two examples above should be food for thought in every divecenter.