I don't see why they don't just allow teams to talk with Free agents after the Super bowl, or the Pro Bowl even. You can still set it up when they can't sign until a specific date, but we all know he is going to be a free agent.
No matter where you draw the line, teams are still going to cross it. And the problem with drawing the line at the Super Bowl is that the teams who are playing deep in the postseason would be pre-occupied with trying to finish the current season with a Superbowl while other teams undoubtedly would already be shopping for players for the next season. I think the system is fine like it is. Everyone has a certain amount of "dead time" to evaluate their current roster and establish their offseason priorities before the next season officially "begins."