Extremely important. And beyond my personal preference, I also believe it's extremely important for physical media to continue being supported in video game consoles as part of the long-term viability of ownership of a license. When you have to depend on a network for the access to your games, your ownership of those games is only as viable as the network itself. Say Sony's PlayStation goes kaput tomorrow and PSN goes kaput with it.... well, all the folks who trafficked with the "all-in on digital library bet" that have hundreds if not thousands of games outside their hard-drives are gonna wake up the following day and realize that such "library" is gone overnight (overnight being a hyperbole - you'll more than likely see it coming but still). Now you can argue... well that's is a worse case scenario bla bla bla. Still it doesn't make the argument wrong.
Physical media doesn't automatically = BD dics. It can be flash drives, SD memory cards etc.... whatever it evolves towards that is also economically feasible.
Full Digital is the path towards no ownership. Digital vs. Physical can be boiled down to trading permanence, and ownership for convenience. I prefer to not do that whenever possible. Indies for example, more often than not force the hand. DLC as well.