Gray fox has a whole story from the end of MG2 to MGS1 that is a blank space. Considering the idea was on the table from konami as well they saw something with the idea. Hes dead but there's still a story in-between those games.
As for Rising the problem I have is that it still tries to be metal gear. The game does a lot of 180 in tones and it's so jarring. Sam was about the only thing that felt consistent and a good middle ground of being best of both worlds. I don't mind over the top, but tone was all over the place. Felt like platinum wanted to go all out but then remembered they can't exactly.
I felt the entire game is tongue in cheek, where the drama revolves around shit that is completely insane.
George got cut in half and then was pieced back together in a matter of hours or days. Raiden getting his eye cut out (which is one of the last body parts he still orignally had) warranted a hearty "damn!". The main antagonist ends up being a United States senator that says he wanted to cause "another 9/11". One of the main conflicts is building child soldiers by taking their brains and training them in VR.
The tone is consistently goofy, jarring, and fantastical.