Benefits of single ospf area
The original question was about advantages of single area OSPF. It seems to me that is really more advantages of multi area OSPF.
I offer the suggestion that an advantage of single area OSPF is that every router or just a 3 layer switch like WS-C3560X-48T-L has full knowledge of the topology of the entire network. Based on this we can say that every router will always choose the optimum path to any destination.
Having said that I will also comment that many things may be seen as an advantage or as a disadvantage depending on how you look at it. The up side in single area OSPF is that routers with full knowledge of the complete topology will always choose the optimum path. But the down side in single area OSPF is that all routers must keep track of all of the details, producing larger data base of LSAs, with more details that must go through the calculations increasing the CPU overhead, and making every router subject to the impact of an interface flap anywhere in the network.
Perhaps we are not understanding the question in quite the same way. It is possible to set up a network with OSPF in which there are multiple area or to set up a network with OSPF in which there is only a single area for the entire network. I understand the original question to be about the latter option.
When there is only a single area for the entire network then the configuration is a bit more simple. And it is true that every router will have full knowlege of all of the parts of the network which would allow it to always make the most optimum routing decision.
Whether these are advantages or disadvantages depends on how you look at it, and probably on the size and complexity of the network you are thinking about. If the network is reasonable small and not too complicated then a single area has real advantages. If the network is larger and more complex then a multi area implementation becomes more beneficial.
There was some source at Cisco which used the number of 50 routers and that number has become very wide spread in discussion of OSPF area size. I would make the point that the type of routers in use when the original statement was made were different from the routers in use now (especially in terms of the memory that they had and the power of the CPU that they used) and 50 is not as good a number as it used to be. I would also make the point that in trying to get the right size of an OSPF area it is more important to consider how many interfaces (how many subnets) there are and how stable or how volatile the network is. Both of these are more significant considerations than having 50 routers.