Where do you think almost ALL of the "illegal" guns circulating in the U.S. came from? That's right: They started off as "Legal" guns. Like you said, most from straw purchases, many from "shady" legal dealers, others from "private sale dealers" and a small % stolen.
Background checks won't eliminate the illegal gun trade but they do make it (at least slightly) more difficult for a violent offender to obtain one. Mostly "career criminals" buy illegal guns. But if you're an everyday Joe, convicted of a felony years ago but bettered yourself, you're not going to buy an illegal gun.
Gun registration, on the other hand, could help reduce the illegal gun trade. It certainly would clear out many of the "shady dealers" and "shady private dealers". Could also help reduce straw purchases since the person buying the gun would be responsible for the weapon. He would (at the very least) need to report the gun lost or stolen and shave off the serial number in order to re-sell it. Many states already have gun registration laws in place.
Why would a responsible, law abiding citizen be against gun registration? I would think the only ones that would be against it would be "shady dealers", criminals, and terrorists, no?
If you own a car, motorcycle, or a boat you need to register it. If you own a house or property, you register it. You need to register to vote in most states. You need a drivers license, which is registered with the state to drive a car. In states that medical marijuana is legal, you need to register with the state for an medical marijuana ID. If you hope to collect social security when you retire, your social security number and benefits are registered.
Why would there be an issue with registering guns?
Wouldn't gun registration help solve criminal cases? If a gun is registered, the police could potentially track the gun and solve the case. The same way the police track down hit and run drivers, etc (By tracking down the license plate).
Wouldn't it also help track down illegal guns? The ballistic "fingerprint" registered with the state would follow the gun for life, even if the serial number is scratched off. And yes, there are ways to file a gun's ballistics but it's not as easy as filing off a serial number nor can it be done with all guns. At the very least, the criminal would know that the gun was registered at some point and could potentially be tracked down. That alone should make at least some criminals think twice.