Basically, navies got out of the habit.
Between the Napoleanic wars and World War I there were very few naval wars. The Russians never had either enough navy or enough merchant marine for the British to chase around the high seas during the Crimean conflict. The Mexicans had no significant navy or merchant marine when the U.S. decided to go settle the southern boundary of Texas as far south as they wanted. Germany had not developed a serious navy when they invaded France–and the battle was confined (pretty much) to land. Neither the Austrians nor the Italians were naval powers when the Italians achieved their independence. When Great Britain decided to impose control on various countries (such as China), it found that they generally did not have modern, European-style navies and their merchant marine tended to be confined to fisheries. The conflict between Spain and the U.S. did not last long enough for any serious commerce raiding to begin. The several wars in South America that spilled out onto the high seas also tended to be coastal conflicts as none of those nations had developed large shipping fleets. When Japan decided to challenge Russia’s Pacific interests, the outcome was decided (as in the case of the U.S. and Spain) in a very short period of time and involved only the navies.
The one war where there was significant merchant marine activity over several years was the U.S. civil war. In that conflict, both types of raids on the merchant marine were carried out. The U.S. boarded and captured C.S.A. shipping (blockade runners) (as well as one notorious incident involving Britain). The C.S.A. sent out a few commerce raiders who tried taking prizes, but as a result of a shortage of crew and hounding by the U.S. Navy, they wound up usually simply destroying the U.S. merchant ships. (Whalers were favorite targets because they brought both necessary oil and income to the Union.) By the time of the next war large enough and long enough to involve attacks on merchant shipping, WWI, a number of changes had occurred.
One big change was steam. Unlike the floating barracks that were used in the Napoleanic wars, warships were built lean and narrow for speed and carried armor to protect against high-powered guns. In addition, the boilers and coal bunkers took up a lot of room in the ships, themselves, where the old sailing ships were like empty barns waiting for men and supplies to be wedged into each nook and cranny. Johnny L.A. is right that ships’ crews (and the room to house them) shrank immensely between 1815 and 1915.
(You’ll notice that the way in which warships fought changed during that same time. It was rather rare before 1820 for a warship to be sunk in battle (and extremely rare for one to be sunk deliberately). The whole method of battle was to overwhelm the opponent with modified infantry tactics, then take the captured ship home to use, yourself. This method was used regardless whether your opponent was a naval or a merchant opponent. With the development of armor for warships, and the response of larger guns firing higher-speed projectiles, far more ships were sunk in battle and the tactics changed to sink them from a distance without boarding.)
So for 100 years, warships got more heavily armed and more cramped for smaller crews. During that time, few commerce-raiding wars occurred, so that the concepts of boarding were left outside most tactical plans. When a major war did resume, what was the primary weapon of choice to attack merchant ships? The submarine. A tiny little pig boat that was smaller than nearly any of its victims with quarters so cramped that most “barracks” were simply converted places among armament or machinery where hammocks could be slung. Where could a prize crew hope to fit? Of course, the WWI submarine was in no position to launch a boarding party, anyway. With a deck down on the water line, coming alongside a merchant vessel (thus placing your torpedoes out of action) was a rather foolish thing to do–especially since the merchant vessels immediately began to sprout cannon of their own so that the threat of a cannon could wind up being a stand-off.
At the beginning of WWI, the British imposed a blockade on northen Europe in which they simply placed a heavily armed cruiser within hailing distance of German ships and ordered them to sail to a British port or be sunk. Since the British could use the Channel and the North Sea as funnels to net German traffic, they did not need to waste crews on prizes–a short jaunt of a day or less brought them to the British port and they could be back on station fairly quickly.
The Germans, however, had to contend with British sea lanes fanning out into the Atlantic (and around the world). They chose to go after British shipping where they could find it, but at the extended reaches of their voyages, they had to settle for sinking the British traffic since they could not keep enough prize crews to make it worth their while. (The Germans began the war with a squadron of cruisers destroying British shipping in the Indian and Pacific oceans, but they were destroyed by a British fleet within four months of the war’s outbreak and the Germans concentrated on submarines after that.) A prize crew would have done the Germans no good in getting the captured prize back to Germany, anyway, since the British would simply sail a cruiser up to it in the North Sea and take it away from the Germans before they could get home.
Once the pattern was set in WWI, there has been no attempt to reverse that trend.