Why struggle for a single pawn? I've seen many chess games, where after a certain point, one side maneuvers their pieces (like doubling the rooks) to target a single point. Most of time it's a pawn on the wing and the other side tries to defend their pawn. But why struggle for a pawn?
As the old poem says:

For want of a nail the shoe was lost.


For want of a shoe the horse was lost.


For want of a horse the rider was lost.


For want of the rider the message was lost.


For want of a message the battle was lost.


For want of a battle the kingdom was lost.


And all for the want of a horseshoe nail.

Exactly the same principle applies in chess. Usually the loss of the pawn results in the loss of the file, loss of control of the file allows the rooks to penetrate and the position soon collapses.