I am with you I love backwards comptibility I use it on all of my games the thought of having a console that can use backwards compadability is amazing .The reason I am skipping PS4 is because it lacks any & all backwards compatibility which is why I got WiiU instead.
Backwards compatibility is a big deal. For example, I wouldn't have bought a 3DS if it didn't play DS games. My line of thinking was: "I want to play DS games but why not invest a little more in a more powerful system that can run DS games as well?"
Now, people got to realize that backward compatibility has a cost, it increases the console price you're not getting it for free. Even in the case of the Wii which has a very similar architecture to the gamecube, you still pay for the controller and memory card slots. That's one of the reasons Nintendo releases non-BC versions of their console later in their life, it decrease production costs, which allows them to increase their profit and/or decreasing the retail price.
Now, if the person is interested in buying a PS4 for playing PS4 games, the lack of BC shouldn't be a problem and it's not a big deal at all