> You may contact us for a refund of the cost of additional seating after travel. If you prefer not to purchase an additional seat in advance , you have the option of purchasing just one seat and then discussing your seating needs with the Customer Service Agent at the departure gate. If it’s determined that a second (or third) seat is needed, you’ll be accommodated with a complimentary additional seat.

From their support page: https://support.southwest.com/helpcenter/s/article/extra-sea...

I have seen them doing that. They give the passenger a placard to put on the extra seat so nobody could sit in it.