I've always believed that one of the strengths of the series is the relative disconnect between the entries. I don't mind individual games being direct sequels, but I think the series would suffer as a whole if you tried to link them together to strongly. Also, that development model really hamstrings the teams who work on it, tending to punish them should they need to change team members, or if someone unexpectedly passes away.
As an example, take the most recent Star Wars trilogy. No matter what you think of each individual movie, whether you liked some or all of them, or hated some or all of them, it's pretty clear that not having all three handled by one person or group of persons who had a clear vision for the total arc of the story really hurt those films. But that's just three movies over the course of a few years. Imagine trying to keep an ongoing series of games on a connected story or timeline. You would just be shooting yourself in the foot.
Also, I've always liked that having them be so far removed from each other lends this feel of them being a collection of apocryphal tales being told or researched by someone. Like, each one of us playing them and having them turn out slightly different is like having different people tell the same story differently.