I have heard the theories that LE wants to interview the parents separately because LE will try to plot one parent against another, that it would be easier for one parent to confess if the other isn't present, or that it's just more intimidating for the parents to be alone.
While any and all variations of the above may be true there is still an obvious, much less manipulative reason why it would be advantageous to interview them separately. Alone, each parent would answer questions with their own words, recollections, thoughts and interpretation of the events. When any and all information could hold great value, it is important to collect as many views of the events as possible. One parent might recall and share something that seems unimportant at the time but proves to be of great value in moving the case forward.
When two people are answering questions together, it is likely that one will answer and the other will agree, disagree and maybe add a fact they think might be significant. But neither will be as detailed in their answers or have the opportunity to give their 100% personal view of the events. Because sitting together and answering together they are providing a "group" view, consciously or not. With most couples I know, there is a leader/follower, talker/quiet balance that is set in place. I can see how that could interfere with information gathering in a group session.
Of course there will be differences in their memories and interpretations but there should be because they will process the input in different ways. It doesn't mean the differences are right or wrong or sinister. It just means there are more details available to LE with which to work. . . and this, IMO, would be a good thing.