I'll hop in there before Professor Bala, who I know will have insightful comments as well.
The reality of the unified family court is that first, it's one-stop shopping. It allows for the litigant, self-represented or otherwise, to go to one court. Second, what has happened, and Professor Bala can probably speak in more detail, is that over the years a specialization has developed, and not just in the courtroom. They are providing family services, information sessions, and mediation. The long-term idea is to have a more holistic situation.
Your underlying premise, of course, is that legal services are prohibitive to the average Canadian and that legal aid just doesn't reach it. Part of the challenge we're going to have, which is not going to be resolved in a day and which this will not solve, is to streamline family law services and make them more accessible and easier to deal with.
These are very contentious and emotional issues, and that goal may not be entirely possible in every case. It probably falls more to the provinces, though also the federal government, to think of innovative ways to address family law rather than work on the traditional model.
I suspect Professor Bala probably has more insightful comments.