While this certainly doesn't need to happen, it can be a hell of a lot of fun.
Back in FFXI, I was part of an RP group that did exactly this. There were 6 of us that went through the CoP mission line together, using the events of the story to form the basis for our own. We were all still part of a larger shell, just had our own substory as well. It was a great experience and lead to some awesome character development. But we while that part of things was kept within the party members (so as not to spoil the plot for others), we kept up regular LS interactions as well.
Long story short, this type of thing is awesome but can work within the setting of a larger linkshell for the best of both worlds.
Back in FFXI, I was part of an RP group that did exactly this. There were 6 of us that went through the CoP mission line together, using the events of the story to form the basis for our own. We were all still part of a larger shell, just had our own substory as well. It was a great experience and lead to some awesome character development. But we while that part of things was kept within the party members (so as not to spoil the plot for others), we kept up regular LS interactions as well.
Long story short, this type of thing is awesome but can work within the setting of a larger linkshell for the best of both worlds.