I'll start with a truism, because that's often a fun place to start as long as you go past it. Any writer, no matter what her professed field of interest, needs to steep herself in the best that literature (and drama, and cinema, and poetry) has to offer.
This is not so she can fall down on her knees in reverence before it all, because that is just as philistine as never reading the work in the first place. It's so she can grapple with it, come away from the experience with something she didn't have before — good, bad, and ugly — and apply that to her work.
I encountered this idea not for the first time but in the way that made the most difference when I read about Macoto Tezuka (Osamu Tezuka's son) offering his services as collaborator on Naoki Urasawa's Pluto, itself a retelling/retake/reinterpretation of Tezuka's Astro-Boy. In an afterword to one of the volumes, Urasawa talked about how Tezuka the Younger insisted that this not be worship, but a wrestling match of sorts — a lively and vigorous dance between two creative minds and not just one bowing down before the other. The results of such reverence are typically boring anyway; viz., my dismay over Tezuka's own Black Jack redrawn by another artist with no discernible reason for the revisitation short of a fast buck on the part of the publisher.
My first exposure to how un-sacrosanct the classics could be was when I had an English teacher in high school turning up his nose rather brutally at Tolstoy. Some of that was, I guess, a defense of one's own turf — he was a Charles Dickens fan, you see — but the mere fact of such a dismissal was a little shocking to my young self. The idea of the classics as being a single, unbroken, homogenous cultural cinderblock took a hammer-blow then and for me hasn't recovered since.
Our attitude towards the best of our own culture should be active, not passive; engaged, not indifferent. Bland affection is itself a form of indifference — it's the indifference of the poseur, the one who loves something out of a sense of unchanging triteness and not because it has the power to (pace Kafka) break up the frozen sea within. We should spit on Shakespeare every so often, if only so that those who love him can muster that much more energetic and thoughtful a defense of him and not remain so hidebound in their own unexamined assurance. I do not say this because I have it in for the Bard, only that I know his work is uneven and some of his plays only have any relevance by dint of being under an umbrella with his name on it.
I mentioned before that things move into the canon in different ways, and for different reasons. We now think of Dashiell Hammett as being no less culturally important than many other authors with far larger pretenses. A big part of why is because we are learning to see these things as a spectrum or a palette rather than a hierarchy. Our compulsion is to fit things onto the rungs of a ladder — as John Cage put it in Lecture on Something: First, Second, No Good — because then, we tell ourselves, that will assign a sense of priorities to it all. Do that and you have created a map to what is most worth studying first, and you can then let all the other useless clabber fall by the wayside.
Sensible as such a plan seems, I think it has failed us, because it has given us excuses to not ask why people enjoy — and find real meaning — in so many things that don't come anywhere near the top rungs of that ladder. It has made us aesthetically deaf-mute to popular culture, with the result that popular culture has gone on and done its own thing, much to the incomprehension of everyone who thought they were stewards of the ivory towers.
Some of this maybe sounds like an argument that professors should get over themselves and see My Little Pony and read Harry Potter just to see what all the fuss is about. They ought to, if only to be clued in. Neither I nor anyone else could convince them to do that; such a thing requires an organic overcoming of prejudices that cannot be commanded. But if they did, they would find that the obverse of my opening premise is also true: that in order to speak of culture, you have to be able to speak of it in the broadest range of its manifestations. It helps for the SF fans to read Dostoevsky and the professors to have at least a passing understanding of Twilight Sparkle — not just so that they can meet in the middle somewhere and shake hands (joybuzzers optional), but so they can depart from their own comfortable terrain into other realms and make discoveries there. What good is it to just sit with one's hands folded?