If I use Panels and Views, do I need to use Blocks at all? My understanding is that if I go the full panels route (i.e. every node is a panel) then I only need to worry about prepping views to populate the panels. Is this the right way to think about it? Or am I missing something in regards to where blocks are still relevant for site building under an all-panels site?
Well, it depends on what your needs are.  Panels and Views is a very powerful combination that can handle almost anything.  That said, there may still be times when you need or want a block.  For example, the Heartbeat and Revisioning modules both supply useful blocks that I use on my (mostly Panels and Views) site.  Yes, these two modules have Views integration, but their built-in blocks are already configured and easier to use than customizing views to meet my needs.

If you need a custom block and are trying to keep things in Panels, you can add a custom content pane.  As a bonus, such panes can be exported with the Features module if you have a complicated deployment.