Privateering is a significant cost saving measure if you have certain specific goals in mind. If you have the specific goal of striking at the enemy's trade networks and the like a privateer can be a cheap way of attempting to do that, you don't have to build or buy the ships yourself, you don't have to pay the crew and given that ships don't last long without constant maintenance you don't have to worry about having to pay for that in peace time. Depending on the specific details of the letter of marque the crown might also get a cut meaning you need to invest very little money while you might get some prize money out of it yourself, at least you get some goods injected into your own economy that might produce some tax gains.

So what you CAN do with them is target enemy trade networks. You deprive the enemy state of some funds with which to wage their war, you may gain some yourself and you put pressure on the enemy government to make peace under what terms you are willing to offer or else its economy will suffer. But they have limitations firstly of a practical nature in what they can do compared to naval vessels. Firstly their basic purpose is to do that which runs a reasonable risk reward, with the reward being prize money. That means they're going to use relatively small fast vessels such as frigates and sloops and they're going to spend their time targeting enemy shipping not for the most part fighting enemy warships if they can help it or doing anything else like patrolling for enemy privateers and pirates to fight and even if they wanted being small fast vessels designed to be able to run away from threats fast and chase down merchant ships easily they can't necessarily go toe to toe with a man of war very easily even if they had the inclination so you can't do things like break a blockade or enforce on stringently or generally take part in fleet actions with them.

A big part of why they came to an end was the Paris declaration of 1856 which outlawed privateering came to be signed by many of the world's great european powers though some like the United states didn't sign. But there weren't as many really large naval conflicts in this period either and as the century went on increasingly the pace of innovation increase as did the specialisation and complexity of naval vessels making it much harder to privately finance a fighting ship and be certain you could make your money back from prize money in any given conflict with the added risk that the ship would have a definite shelf life for its usefulness before it was too obsolete and would be unable to outrun anything that could outgun it and out gun anything that could outrun it as had always been the aim with frigates and the like of the age of sail.