The problem isn't necessarily that they force copious story-based limitations on the gameplay (although that is a big part of it), it's that the story that they are sacrificing the gameplay for is just not that good.
Options
1. Go back to the classic GTA craziness. No compromises. Sure, Saints Row has enroached on this niche, but with 3-4 year development cycles for both series, they can co-exist.
2. Keep the seriousness, but make gameplay the top priority. Perhaps having the main character go on rampages - or wear something other than a jacket - may compromise the 'realism' of the story, but who actually cares? GTA has always been a game about freedom and violence, and 95% of your audience plays it for that: the parts in between the so-called 'story'. Pay attention to the atmosphere, but if a 'story' element compromises the fun that a player can have, it goes out.
3. Keep the seriousness and focus on story, but hire professionals to make a story worth giving a shit about. That's right, if you're going to make us sit through hours upon hours of conventional movie scenes, make sure they are written by PROFESSIONAL WRITERS, and directed by PROFESSIONAL DIRECTORS. In this day and age, you are competing with every movie, TV show, book and music album in existence; you need to be at that level. No more dialogue written by game producers, or cutscenes edited by CG programmers, please.
4. Combine all the above approaches in one game. For example, you could use multiple playable characters; one character's story could be all out crazy, another character's could be realistically restrained, and so on. Or even have stuntman side missions, wherein you act out various over-the-top action scenes on a Hollywood set or on location. Choice: the one thing that separates games from every other medium.
