The SEC gives teams huge dollars from the TV broadcast revenue.
Take the king’s coin, do the king’s bidding.
But once per decade or so, the programs might willingly pay the fine if the field storming helps market the win as a legacy win. For example, Vols fans will probably many years talk about the time they stormed the field, tore down the goal post, carried it down the street, and threw it into the river after Tennessee beat Bama for the first time in a dozen years. Sure the Vols had expenses for both the fine and repairs to the field. But it was worth that expense to add to the "Remember when..." folklore of the win that they can market on for a while.
A few years back Tennessee fans stormed the field after beating Alabama in football. They raised the money to cover the fines before the people even left the stadium. To them, it was worth it.