As briefly as possible, it's because the missions are not just about military. They recognize and work on the connections among insecurity, governance problems, and development problems. It's because in spite of the fact that everyone criticizes the UN, including Malian actors, when you get them in a room and talk to them, they will recognize that the UN doesn't have the kinds of direct interest that other countries have in a specific outcome in Mali beyond just peace and security.
Algeria negotiated the agreement because, to put it bluntly, the Algerians didn't want to see another insurgency at their border. Once they started being concerned with Libya, their concern was to finish quickly with Mali so that they could turn to Libya. That haste is part of the reason we have an agreement that is half-baked.
In other words, no one except the UN, if funded and supported, actually has the interest and the willingness to stay the course. Other countries either achieve their interests or move away. It seems to me it is because of this that the UN continues to be the best bet. It's also because the UN is the only place where all of the other countries with interests can actually come to talk.
The UN is thus the place where G5 Sahel members or the French or whoever sort out their differences and reach agreements. We saw this when the UN initially did not want to back the G5 Sahel force; then there were discussions in the corridors and there was some backing provided.
The UN continues to be the place where the various actors with specific national interests can actually talk to one another. No other organization or actor can provide that kind of convening power.