No, I'm only talking about compound paths or subpaths. As far as I know, the only way to connect separate simple paths, is with snapping. Here are 2 simple paths:

There are no tiny squares for the Pen (Bezier) tool. However, if you use snapping (nodes and handles to cusp nodes), you can use the pen tool, and the click on node #1 continues that path. A single click on node #2 does not end the path, but a double-click on node #2 has the exact same effect as in my original message -- and extra node, right on top of node #2. And then can then be joined with the Node tool (Join).
That makes sense that there's an extra node, because the double click should create an end node. But in my example, it only takes a single click to "close and finish the path". It just makes sense to me that there should not be that extra node, which requires then the Node tool to Join the 2 remaining end nodes. Otherwise, why does the single click "close and finish the path", but still add the extra node?
In my simplistic example in the original message, using the Node tool and "Join selected endnodes with new segment", absolutely is the best solution. But the problem I'm having, is that I might have drawn several corner nodes in between the 2 paths I'm connecting. Like so:


Yes, I see what you're saying, that using the pen tool to close a path, does not result in an extra node, or require the extra step to join the 2 end nodes. I just can't understand why it only works to close a closed path, and not to join 2 subpaths. I think maybe it should. Does anyone know any good reason why it should not? Maybe I'll report to Launchpad?