I'm having an epiphany of sorts.
For a very long time, I thought that the idea of "race as class" was just plain weird. Why couldn't a dwarf be a fighter? Why can't a hobbit be a thief? It seemed very strange to me, reading about this in Moldvay/Mentzer Basic D&D. "It's about the focus of the game" people would say to me. Still, I couldn't quite wrap my brain around it.
When I got Advanced Edition Companion, I found myself thinking quite happily about all the different classes and races I wanted to have available for play in my new campaign. I began to realize that - far from being an "either/or" choice - multi-classing and "race-as-class" were both acceptable, and depending on what I wanted, highly appropriate for my campaign.
I'm going through some of my thinking about this over on the ODD74 message board. Feel free to stop over and add a comment or two.