The reason this doesn't work, apart from risks of price fluctuation while you hold the bitcoin, is transaction costs. Bitcoin has gotten a lot of attention for being a cheap way to process payments, and while that's true if you already have bitcoins and you're sending them to someone else who is going to keep them as bitcoin, high costs of swapping bitcoin for regular currencies are probably inevitable. Bitcoin transfers are irreversible, which means there is a huge potential for fraud. Once they've sent you the bitcoin, they have little to no recourse against a chargeback. And the person who fraudulently obtained the bitcoins can easily launder them through untraceable transfers between many different addresses before cashing them out, so the risk of being caught is probably a lot lower than other forms of CC fraud.
Not only could the card be stolen, but even if it isn't, I'm sure there are friendly fraud concerns as they would have a hard time proving you received the item purchased. To some extent they can mitigate fraud with a waiting period between placing an order and receiving the bitcoin, verifying billing address, etc. but they can't stop it all so they have to charge high fees to cover their losses. Anyone can start a bitcoin exchange so if the exchange fees were too high, competition would drive them down. The worst part is as fees rise, it drives legitimate buyers out of the market, but not fraudsters who don't care about fees, creating a negative feedback loop that makes things worse.
Not to mention in addition to the CC companies not being too happy about all this due to fraud risks, large amounts of transactions swapping bitcoin for USD will probably draw unwanted attention from the feds since they know well about all of its untraceable characteristics. We already look enough like terrorist financiers/money launderers to them without adding large bitcoin transactions into the mix.