Many gun thefts are crimes of opportunity/passion like you say, but not all. Most violent offenders don't steal the guns they use to commit crimes they buy them from the black market. Promoting a black market opportunity is a very dumb policy.
An old (circa 1997) U.S. Department of Justice survey of prison inmates possessing a firearm during the offense that put them in jail showed that only 14% bought their gun from a retail store, pawn shop, flea market, or gun show. 40% acquired their firearms from family or friends. [0] The remainder were stolen or purchased on the black market. I can't say whether recent trends are any different, it's not my area of interest anymore.
The FBI compiles data on the theft of guns through the Stolen Gun File of the NCIC database [1]. I haven't had access in a long time but when I was doing research many years ago I found that between 1992 and 2002, around 1.7 million firearms were taken, representing a rate of 16.8 stolen firearms for every one thousand households. Of those stolen weapons, 687,857 were later recovered by authorities or by "guns for x" amnesty turn-in programs as of 2002. So that means more than one million of those stolen firearms were unaccounted for as of 2002.
[0]: Caroline Wolf Harlow, Firearm Use by Offenders, Bureau of Justice Statistics, November 2001 (sorry no link available that I know of)