So, every other Alfred in the movies, and the version in the comics for decades doesn't care about Bruce because they don't constantly nag him and try to get him to quit? Alfred can care and worry about Bruce, and still support his mission. In the end, batman never quits. He's Batman until he dies. Nolan didn't get it, but I don't think he "got" Batman any better then Joel Schumacher did, he just missed the point in a different way. His Alfred was part of that.
I think that's one area where Snyder "gets" Batman a bit more then Nolan. Now, obviously Batman doesn't start killing people, which is where Snyder's version went off the rails, but a Batman who just keeps getting older and probably harder/colder but still keeps up the fight as the years go by (with an Alfred that stays by his side and may want something different for Bruce, but still supports him and doesn't whine constantly) makes sense, more then "Batman quits for stupid reasons, comes back then quits again because reasons and goes off with Catwoman". Even though Snyder probably took that older, harder Batman attitude from The Dark Knight Returns (which went a bit too far with it), it still feels like Batman to me (minus Snyder's Batman being a mass killer).