In simple terms, yes and no.

Strategic bombing during World War II was a new art and the US and UK had previously never done something like it. The idea of bombing civilian populations however came up around in WW1 during the zeppelin raids on England and it was generally frowned upon. But World War II was a new war and it was demonstrated by German air attacks in Poland, Rotterdam and London that civilians were going to be free targets.

“Terror bombing” was a word that FDR hated but church hill didn’t mind using it and actually kind of liked it. In the west the strategic bombing campaigns primary objective was to see the destruction of the German war machine. Allied targets would be anything that provided support to the German war machine, as you may guess these were in cities which obviously held a lot of civilians. So the allies could launch their bombing campaign and kill civilians as well as destroy their targets or do neither and have a more difficult time defeating the Germans, they choose the former. Civilians were not the main goal, it’s important to stress that, at least for the early strategic bombing campaign.

Now how well did it break German moral. Well first off, it definitely crippled the German war machine, or at least slowed it down. The Germans were notoriously good at both defending and rebuilding their factories. US bombing raids for example had to stop as late as February 1945 do to heavy losses in the campaigns. German moral was also affected. Germany hadn’t seen this kind of destruction before since World War I wasn’t really fought on their ground. Houses and shops and entire cities became destroyed and this did have an affect on the German population. But we must remember that Germany was under the rule of a dictator and propaganda made a huge appearance. After the bombing of Dresden, Joseph Goebbels launched a massive propaganda campaign about how the bombers were purposely targeting civilians and destroying German cultural landmarks, basically saying “they want to destroy Germany, so you know... don’t surrender and fight harder” in reality Dresden was a fair target as 40,000 German soldiers passed through it daily on its railway and it supplied much of the Germans army group center during the period it was bombed, ironically enough this rumor persist to this day.

So propaganda definitely played a big role and much of the strategic bombing affects on the civilian population did not have a massive affect on Germany as a whole, that being said it definitely was partly a reason many Germans wanted to end the war. After all, when Allied bombers were shot down, the pilots and airmen were not taken prisoner as often as you may think and most of the time they were lynched by the locals.

Now Japan was similar and different. The US again did not consider civilian losses but also were aiming to inflect casualties on the Japanese civilians. The bombing campaign started later than it did in Europe and the Japanese had shifted tactics on the frontlines to become more defensive minded, and often fought to the last man. The US knew it wasn’t going to be easy and had two primary objectives, destroy the Japanese war machine and destroy the Japanese will to fight ( by bombing Japanese cities directly ) and factories were in cities which made it easy. It had a massive affect on the Japanese war machine, so effective that Japanese home guard units were forced to train and if US forces invaded, fight with black powder weapons. And many weapons found on Okinawa were single shot rifles, a product of a extremely successful US bombing campaign ( they learned from failures in Europe )

But how did it break Japanese moral. The firebombing of Tokyo on March 9th-10th was probably the most destructive event in human history, I’d personally argue even worse than the atomic bombs. The mostly “paper city” that is the city was made out of like a paper like material which many Japanese lived in, was basically wiped off the map. I think Haruyo Nihei, an 8 year old girl at the time sums it up best

"I remember seeing other families, like us, holding hands and running through the fires," she recollected. "I saw a baby on fire on a mother's back. I saw children on fire, but they were still running. I saw people catch fire when they fell onto the road because it was so hot."

Anywhere between 100,000-300,000 civilians died and another million was displaced. This had a massive effect on Japanese moral. And other cities were bombed, but not to this extent ( unless you count the atomic bombs )

But like Germany, propaganda played a huge role. A sizable part of the population did want to surrender but a large amount didn’t. Japanese propaganda to its civilians said things such as “the US Marine divisions are units made to rape Asian woman” and that US troops would slaughter and torture Japanese civilians for fun ( ironically the Japanese did that at Nanking and Manila... ) and many wanted to fight to the death out of fears of such acts.

The US tried different solutions and halted its bombing campaign temporarily in the summer of 1945. Leaflets were dropped on Japan that read things such as this

“On Saipan 26,000 Japanese soldiers suffered an honorable defeat. On Iwo Jima 23,000 Japanese officers and men died a tragic death. In the Philippines, more than 410,000 Japanese warriors are dead. And on Okinawa, which fell 21 June, a total of 105,000 officers and men in the Japanese forces perished in battle.

The Japanese armed forces, which rely upon spiritual strength, can in no way compete with the Americans whose material combat strength is inexhaustible. Moreover, it would not do for the American armed forces, no matter how sorry for the people of Japan to allow a war to end so long as the Japanese forces, whose policy of aggression and lust of conquest have plunged mankind into the horrors of war, are not made to cry “we surrender”

The Americans will therefore relentlessly carry out the invasion of the Japanese homeland. Already the island of Okinawa has been transformed into a great base for bombing of the homeland... a foothold for American landings on japan as been secured, its only a matter of time... those American heroes who have already beaten Germany are coming closely upon you. The depths of the misery into which your country will be plunged into by the fearsome destructive power of modern warfare cannot be fathomed... but there is a way to escape this destruction, and that it goes without saying, is for you to surrender”

Sorry for the length. But you can see how the US really, really didn’t want japan to keep fighting. But they were surely going to continue the bombing campaign later on in the war if japan didn’t surrender in the summer, which they did of course.

In summery, the Allied bombing campaigns of the war were successful in destroying the war machine, and yes it didn’t make both Germans and Japanese want to surrender. But propaganda mitigated how other parts of the population were taking it and many, at least in japan still wanted to fight on.