I'd like to know what the benefits of this are other than maybe a simpler strategy for load/store operations (...)
The benefit is that you don't need virtual memory, which makes this concept work on the simplest of CPUs/architectures. Also you don't need an operating system that keeps track of memory areas and their assignment to programs. In other words, such an implementation is well suited for e.g. small-scale embedded systems that typically don't have (and don't need) the processing power of a modern day desktop or server CPU.
(...) because you don't need to distinguish between two different memory areas.
I suppose by memory areas you mean the concept of multiple contigous memory spaces which are separated such that they each have an address range of relative indexes (0, ..., n)
where n is the maximum number of bytes in that area.
That makes a lot of sense if you have virtual memory, that is the CPU implements a layer on top of the physical memory that gives programs the illusion of each having a seperate, contigous memory space.