That Wikipedia link seems to support the claim that lighthouses actually failed to operate well without government intervention:
"Eventually, all these rights were withdrawn or bought up by the authorities because the total light dues that had to be paid by ships were too high as a result of rent-seeking activities of these so-called private providers of lighthouses. Barnett and Block (2007) qualify these critiques by showing that private lighthouses are possible, but do not show up in the historical record."
"Eventually, all these rights were withdrawn or bought up by the authorities because the total light dues that had to be paid by ships were too high as a result of rent-seeking activities of these so-called private providers of lighthouses. Barnett and Block (2007) qualify these critiques by showing that private lighthouses are possible, but do not show up in the historical record."