Glad i'm not the only one struggling with this.
Another case where the new selection system fails is when you use left click select and a gizmo is active. Since you can't select the specific bone you want with a single click anymore, the gizmo will now appear under the cursor and you can't start cycling through bones. This leaves you with scrolling, rotating around the bones or tool changing to either find an angle where the gizmo is not in your way or get rid of the gizmo for a moment.
The old selection understood and supported the users actions. The change feels like a huge step backwards, making selections tedious and more time consuming. By the amount of selections that are made while rigging this really adds up.