Thanks for the tip, Jeff.
So, the example was a little contrived. The more likely scenario is one in which I have 3 consoles all connected to the receiver via HDMI, and then a couple of assorted peripherals attached via their best interface; so, cable box or streaming device over component. I wanted to know whether other users of the whole AV system would need to have deep knowledge of the system's topography, and possibly know whether a given source switch necessitated fiddling with the TV vs. simply switching via the receiver.
My old receiver (~10 years) just died in a brownout, and I'm having to learn all this stuff over again as I look at upgrading. A lot of these things weren't available (or at least weren't relevant to me) back when all I had to do was plug my Xbox, PS2, and N64 into my CRT. 8)
Trying to figure out how many HDMIs inputs is the acceptable minimum, given my current and planned source list.