"The British went to the peace table because their income went to zero."
You're joking, right?
Yes, American privateers captured a significant number of English merchantmen.
But, just how much of an effect did that really have?
In the grand scheme of things, virtually no real effect on the British.
Their merchant fleet was simply enormous, and most of it was untouched by American privateers. There were simply too many English merchant vessles and too few American privateers. As well, many of the ships that were taken were smaller coastal trade ships,
In counterpoint, the Royal Navy blockade of the American coast, hurt American commerce FAR more than American privateers hurt British trade.
After 1813 American sea trade virtually ceased in most ports of any significance.
At best, this aspect of the war can also be seen as more of a push than as an American victory.
Yes, American privateers captured cargos of significant worth, but that was more than offset by the losses in foreign trade.