The Falcons do not have the personnel to run a 3-4, they don't have the draft picks or cap room to make the transition, and they would annoy a good portion of their fan base by hiring away Georgia's defensive coordinator. Other than that, the move would've made perfect sense.
Let's think about all of the reasons why the Falcons would not offer their defensive coordinator job to Todd Grantham, who's denied rumors of interest on his part:
1. The Falcons do not have 3-4 personnel. There isn't a true space-eating nose tackle on the roster,* their defensive ends do not seem like good fits to become 3-4 ends, and Sean Weatherspoon, the team's best defensive player this year, doesn't seem to have a natural position in a 3-4. The only player for whom the move would make sense is Ray Edwards, who has been a 4-3 end for his whole career, but given his lack of pass rush as well as the fact that the Falcons' run defense was the best in the NFL in his area,** he fits the profile of a 3-4 end, at least performance-wise if not physically.
** - That stat is the reason why I am hesitant to label Edwards as a free agent bust.
2. The Falcons mortgaged the future to acquire Julio Jones, so they do not have the draft picks necessary to change the defense from a 4-3 to a 3-4.
3. The Falcons have a lot of free agents in the offseason (and not necessarily the ones that they would look to jettison if they were transitioning to a 3-4). This offseason is going to be difficult enough in terms of roster management without piling onto Thomas Dimitroff's plate the requirement that he acquire the various parts needed to run a different defense.
4. The Falcons are set up to win now, so taking a step back to change directions on defense would make no sense.
5. A significant portion of the Falcons' fan base is comprised of Georgia fans. How exactly do we think that Georgia fans would react to losing their now-beloved defensive coordinator to the local pro football collective right before a season in which Georgia will be preseason top ten and expected to win the East and challenge for the SEC title? Arthur Blank didn't get to where he is by angering his customers. It would make a lot more sense for him to back the Brinks truck up to Steve Spagnuolo's house so the Falcons can sell their fans on the fact that they hired a Super Bowl-winning defensive coordinator.
If I had to speculate, I'd say that Pete Roussel took a wild-ass guess here: the local NFL team needs a defensive coordinator and the local college team has a guy who had a great year, so obviously, the NFL team would try to hire the college coordinator. If you didn't know the relationship between SEC football and the NFL in this market (not to mention the local NFL team's defensive personnel), then that would be a reasonable guess.