There are very few airside kiosks on Southwest or any other airline. People just line up to see the Gate Agent at the podium. IMHO Southwest would need to triple its staffing for Gate Agents to handle assigned seating.
"Triple its staffing" to handle assigned seating?
No way.
I seldom see more than one GA at FL gates - even on full flights. Sometimes an agent at an adjacent gate will staff the desk while the arriving plane is met and the jetway is moved. More often, though, the desk is empty during de-planing and as flights are checked for those w/connections.