ppl do that all the time, and even make a living off of it. of course, they sell ALL the cards, not just the valuable ones. when i played, packs cost $3, and you could sell commons for a dime, uncommons for a quater, and rares for a dollar. these prices would of course be much higher for valuable cards, some rares could go up to $5, and even some commons and uncommons could sell for a dollar if they were sought after enough. note btw that mythic rares didnt exist back then, and i have no idea what pricing is default for cards today.
irregardless, often you can buy a pack and sell the individual cards in it for more than the pack was worth. hell, the precons at the time sold for $10, even though all the cards they contained could easily be sold for $20 or more. of course, the only person i know of that did that actually owned a magic shop, so he was probably only paying retail for them, thus giving himself a wider profit margin. how else do you think stores online get their cards? they get them out of packs just like everyone else.
edit: of course, if you wait a few years cards become more and more expensive the longer they've been out of print, and their price skyrockets if they're valuable in the tournaments for the lower formats. even some old commons can sell for $10. rares can easily go over $100. but that takes years to happen, the profit may or may not actually be worth the time it takes to build up, i dont know.