There's a lot of reasons to continue the Metal Gear Solid franchise, but unfortunately, there's as many not to. Without Kojima, it would seem that a Metal Gear Solid 6 could never live up to its predecessors, which is a big enough problem to end the conversation for many.
However, looking at the games as a franchise alone without the real-world concerns, another big problem rears its head. It could easily be fixed or retconned (which is admittedly partially the problem), but part of it comes down to one character in Metal Gear Solid 5: The Phantom Pain, Venom Snake.
Venom Snake and Big Boss
Without a doubt, Venom Snake's character arc in Metal Gear Solid 5 is well put together. It's an interesting evolution as players learn that they are not big Boss, but a medic who took shrapnel to the face and was subsequently implanted with Big Boss's memory. Venom Snake eventually learns this, and in true fashion, ignores it because it means it's all part of Big Boss' identity. For players, it's an interesting revelation, and it even comes with an interesting retcon to the franchise.
Separating the two (Venom Snake and Big Boss) in the franchise is actually somewhat difficult, with many of Big Boss' "former" accomplishments actually being "attributed" to Venom Snake. However, there's one moment that was almost certainly originally Big Boss, but then it was Venom Snake after Metal Gear Solid 5. Solid Snake kills Big Boss at the end of the first game, but now it turns out to be Venom Snake. As such, Venom Snake is the first Snake to die, having living in the shadow of Big Boss for so long the two characters were one in the same all the way to his death. Venom Snake lived as he died, building the legacy of Big Boss, and that's a symptom of a unique problem for MGS6.
The Problem with Metal Gear Solid 6
Even being as conservative as possible, there's at least 40+ retcons in the Metal Gear Solid franchise. The revelation that Venom Snake is Big Boss doesn't necessarily change the overarching story, instead fitting in quite nicely, but it does add more to it. There's a lot to be said about war and history in how the games interconnect, but regardless how casual or hardcore a fan is, it eventually becomes hard to keep facts straight. The whole story becomes more convoluted the more someone thinks about it. As such, Metal Gear Solid 6 would be yet another entry indubitably creating its own retcons.
When storylines become so complicated, they become harder to follow without tripping over toes. It would likely be difficult for Kojima to keep it all straight, much less any new developers or even others at Konami. This could be anything from a time period and event which contradicts another, a game taking place in between retcons and the events become muddied, or a game taking place so far out that it's not a problem but becomes a problem for its connection to Metal Gear Solid. It's not a win-win, and while Venom Snake is only one symptom, it's a punishing one.
Metal Gear Solid 6 is not known to be in development.