If a layer or a group has an level effect applied (in this case it’s Transform, for creating symmetric designs), then Ai doesn’t apply random size for the calligraphy brush tips created with Brush tool inside this group/layer — but does it outside of this group / on a normal layer.

Take a look at the test file attached and the GIF recorded.
Clicking with Brush tool randomizes the size for the first object created in Layer 1 (with the effect applied), but each consequential click makes points with same thickness.
But when the same happens on Layer 2, with no effect applied, each tip is random.

Thanks to e.k. kuzey for bringing this up.