The problem is that the steps legit people would have to go through to make a purchase are an extreme hassle.
If folks absolutely need to use a line of credit, it's just going to be easier to get a cash advance and use something like BitInstant.
Good point , it becomes a hassle for people legitimate customers wanting to use a CC for convenience. It basically goes against the whole point of convenience.
Not to mention the extra fee's customers would have to pay to make up for cc transaction fee's a provider would need to recoup. This is in addition to the normal exchange fee's a service would charge. So suddenly your paying high fee's for something that in the end is just as convenient as other options available with less fee's.
Also the process of providing ID and a phone (which you can later claim was stolen) isn't enough to deter a criminal from making a quick buck. If I know I can buy 5 bitcoins (about $1,000) and I can get my money back and keep the coins simply by telling my CC company that my car or house were broken into. I will gladly fill out the proper ID info.
So in the end.... you end up driving away most legitimate customers but create a gold mine for scammers. This is why CC > BTC wont work and it's why no one is trying it.