Using Matrix[i,j] is the most intuitive way for most people. It's what you'd use if you don't know anything and it's what you'd understand immediately. That's the benefit for the user.
And to be honest, in the list of things that the C++ folks seems to think is important, multi-index index operators seems like it would rank substantially higher than a lot of the other things in the list in terms of value, and a lot lower in-terms of additional complexity.