Long ago I wrote a post about having a Halo 4 sometime in the future, like 10 years from now. It would be good to have a game where the plot is that Master Chief is being woken up (is that right, woken up?) from cryo sleep to deal with a new threat in the distant future, long after the end of Halo 3. It would have to be a truly great game, long, epic, with a good story. And there would need to be only one, let it go after that. If this idea is brought to fruition, Halo and Master Chief will be true legends, the stuff of mythology in the modern age.
Thing is, that's the key: do it a long time from now. Now, or in a couple years from now, is too soon. If they make a new Halo game now, it will just seem like fan service, like Star Wars: the Clone Wars, or some similar fanboy festival. Do it in say, ten-fifteen years, that'll be great.
As for the developer issue, I say let any developer do it as long as it's a good developer, especially one experienced in making FPS's. The name of a company doesn't make a game, it''s the work that gets put into it, the attention to detail, the quality of gameplay, the graphics, and the story.