Purpose of small white triangle at top-right corner of a layer (in layers panel)?

It's just an indicator that tells you that the highlighted item in the palette is a main layer or a sublayer. It can be helpful if you are working with nested layers that contains a lot of sublayers and groups because groups are not marked with the triangle.

It's not necessary to click on the triangle to select all objects on a layer. You can just click somewhere in the right column of the layer item.