Most things are already mentioned. Just some comments:

If you talk about carpet bombing you talk about bombing of cities, not troops, right?

The theory of massive air strike against towns was developed after WW1. Douhain wrote, that in the next war big air armies would fly over the immobile armies and directly attack the cities. No country would stand these attacks. The people would revolt against their government. It was an idea of a strategic and psychological air war.

Many nations adopted the idea, for example Britain and the US. For Britain it seamed to be the perfect strategy. They sat save on their islands and could attack the continent without the extreme casualties they had payed in WW1. On the other side Britain had to protect itself against air attacks. So they had a strong focus on air defence and strategic bombing.

The Axis countries never implemented a strategic bombing. The Germans decided to build the Luftwaffe as a close support weapon for the Heer, completly tactical focus. The idea was to beat the other countries in a series of seperated lightning strikes. This was the German concept after the lessons of WW1. I guess the Italians did not develop strategic bombers because they had not the capacity to build the bombers.

Before WW2 the effect of cty bombing was overrated, as well as the strentgh of the luftwaffe. Hitler coulf threaten the Austrian and Czechoslovakian governments with potential air strikes against their capitols.

In the beginning the Germans used city bombing only because of terror. They thought that their enemies would accept the uselessness of any resistance. (Warzaw, Rotterdam). However, city bombing was not a central part of the German strategy.

When the Germans finally had reached the Channel, they simply did not know what to do. Hitler had never thought of the necessarity to attack England and neither the Army, nor the Luftwaffe or the Marine hasd any plan. They started to bomb southern England. However, the targets were strictly limited to military objectives, factiries and ships. There were several orders from Hitler to avoid bombing of civilians.

He changed his position when he saw that his attacks against military targets did not bring peace and that the Brits bombed Berlin. He hoped that the Brits would give in as soon as the bombs would hit their capitol. So the target was terror. However, the bombing did strengthen the will of the British to fight on.

After that the British started their bombing against Germany. They had to find out that the accuracy of the bombing was much worse than expected and that the casualties were very high. So they had to change their strategy from attacking military targets at day to attacking civilians at night. In my opinions they changed their strategy because they had to do something (it was the only way to attack the Germans) and made a jusstification for it later. They openly said that the target was to kill as many Germans as possible. This would reduce the manpower at the front and in the industry.

When the US entered the war, they first followed the concept of daylight bombing, with some success. Later they changed to terror bombing too.

There are two basic issues left:

1) Were the attacks justified?
2) Were they usefull?

1) In my opinion - no. Attacking civilian is never justified, regardless if it is done by Germans or British. It is a war crime!
P.S.: This does not say that the Germans did not do other war crimes and other crimes (mass murder).
2) They had impact on the German production. However, they also wasted a lot of resources from the allies. I think the Allies could have used their resources much better. For example to dominate the Med from the very beginning. To Japan: I still believe that Japan would have had to capitulate just by cutting off the sea connections. Japan has no natural resources and pruduces not enough food. So why attacking the civilians?