The most obvious advantage to linking to the main story is that it gives your narrative coherence. As each subplot moves forward and resolves, its resolution can help construct the overall conclusion of your story. The second volume of "The Lord of the Rings, The Two Towers" is an example of this approach. Aragon, Legolas and Gimli's encounter with the Rohirrim sets up their presence in the climax of the next book, while Pippin and Merry's encounter with the Ents leads to the resolution of the Saruman plot line.
"Enduring Love" by Ian McCewan uses linking back to the central plot as a means of exploring the consequences of events on the characters. The novel follows Joe Rose and Jed Parry, two men who attempt to stop an accident. In doing so, Jed becomes obsessed with Joe to the point of threatening his life. One of the subplots involves Joe's long-term relationship collapsing under the weight of Jed's presence. This neatly demonstrates the consequences of the book's central plot.
The principal disadvantage to linking back to the main story is that it makes character subservient to plot. If this happens, your characters will be perceived to be acting in a manner which serves the plot first and makes logical sense second, with the need to reach the next big "event" outweighing the characters' own perceptions and desires. Dan Brown's novels, notably "The Da Vinci Code," have been criticized for this practice.
Tidy plotting and linking back to your central plot has a lot to recommend it, but when taken too far, it can damage the drama and conflict you've set up. By linking everything together, there is a danger that your story will appear to be built entirely on coincidence. In certain circumstances, this can work very well. Louise Wener's "The Perfect Play" is a good example of this. The novel follows the daughter of a gambler as she becomes friends with a former gambler, learns to play cards and ultimately finds her father, still gambling, in America.