Based on the article, yes.

Usually runoff to a nearby river, taking a lot of soil nutrients with it.

Many engineers know about it, the 'problem' is that it takes a lot of time, unused land and man/machine labor to build. If OP and I watched the same documentary, it took a whole village months to build these wadis in areas that weren't being used. Other places that similar techniques are being used on private land for those that are willing to spend the time to experiment based on the needs of that area.

In the US there are beaver relocation programs - beavers don't build wadis but they do build reservoirs and wetlands that give the same result. Same downsides. Beavers can build in areas that can cause flooding and damage to other infrastructure. Identifying areas that would benefit having beavers building dams and the relocation process take time, effort, coordination and money to complete.

Thank you, that was what I was looking for!

Could you give a source on that? Really interested in more.