I've said it before, but GTAV feels like it's Michael's and to a lesser extent Trevor's story, and i do believe that was the original intention. Who knows why they went with the three protagonists route in the end.
When you look at every single story beat in this plot, most if not all of them are related to Michael's plot, with Trevor being more of a side character and Franklin just being... There. Only thing he has going is a different viewpoint coming from the hood, but even then, he moves out of there very early on and becomes "The Sidekick" from there onwards.
Frank just didn't have much to do, he wanted to be more than a just hoodlum, he earns that about 6 missions in or so. Even his role during the final mission seems too contrived for me. You're telling me these two different parties with access to sufficient firepower just suddenly decided "Nah, let's get that one single nigga we barely even know" to clap their respective targets? Hell, if you go with The Third Way even Franklin himself is surprised when the game decides to throw Stretch in as his final enemy.
In short, Franklin's story has no urgency because he barely had a story to begin with