Hi Bob. Welcome to our little corner of the 'net.
The short answer to your question is that is just doesn't matter where the router is mounted in your table.. it comes down to personal preference. The bit is round, so it will cut in any direction. Of course, when using a fence, stock moves from the right to the left across the face of the bit.
Most pieces being routed are small, so you don't need a lot of surface area for support. For those times you are routing large pieces, you can turn the fence around and use the full table to support your work. This is also one of the advantages of using basic c-clamps to hold your fence in place and not t-track.. the fence can go ANYWHERE on the table and be secured by the clamps.
Sometimes I wonder whether the world is being run by smart people who are putting us on
or by imbeciles who really mean it.