Channels in convolutional layer
The technique you have mentioned is called "Depth-wise Separable Convolutions" and it relies on the idea that spatial and depth-wise information can be decoupled. Its main advantage is that compared with standard convolution, since it doesn't need to perform convolution across all channels, it has considerably less connections, (so less parameters) which results in a lighter model.

There is an architecture named "Xception" ("Extreme version of Inception") by Google that uses a version of such convolutional layers and produces close to state-of-the-art results. There is a really good review of it at Towards Data Science.

Personally I don't like the idea of decoupling the channels, because I think it gets us a less "sophisticated" model, but it seems to work so who am I to judge?