The ETO for US doctrine was a different story. Dresden was the exception.
As soon as the 8th AF got their first bombing radars in 1943 they began area bombing German cities. They did so because on cloudy days they had difficulty hitting other targets and because cloud cover helped reduce their losses.
Sometimes they took off with a German city centre as their assigned target. Other times they followed standing orders which let them bomb any German town as a target of opportunity. From the standing orders, acceptable secondary targets at various times:
"Any German city which may be bombed without disrupting the Fighter Support", "Any industrial city positively identified in Germany", "Any city positively identified as being in Germany which can be attacked without disrupting fighter support"
Standing orders were later changed to:
No towns or cities in Germany will be attacked
as secondary or last resort targets, targets of
opportunity, or otherwise, unless such towns contain
or have immediately adjacent to them, one (1)
or more military objectives. Military objectives
include railway lines; junctions; marshalling yards;
railway or road bridges, or other communications
networks; any industrial plant; and such obvious
military objectives as oil storage tanks, military
camps and barracks, troop concentrations, motor
transport or AFV parks, ordnance or supply
depots, ammunition depots; airfields; etc.
It has been determined that towns and cities
large enough to produce an identifiable return on
the H2X scope generally contain a large proportion
of the military objectives listed above. These centers,
therefore, may be attacked as secondary or
last resort targets through the overcast bombing
technique.
In other words, if you can see it on radar, bomb it.
The 8th AF certainly wasn't "enthusiastic" about bombing civilians, though. At the time they admitted to area bombing cities, and the orders and post raid reports show that, but by the end of the war they were using the euphemism "marshaling yards" to hide their area bombing raids, and their post war reports made no mention of the area bombing attacks they had ordered.
I'm sorry - the US doctrine of precision bombing in Europe might have served to soothe consciences back home but it didn't make much difference to German civilians. I believe the USAAF routinely bombed through cloud using radar in the last two years of the war – how could that be anything but bombing of a civilian centre?
I believe the majority of bombs dropped by the 8th AF used radar aiming. Accuracy was very poor. When dropped blind through complete cloud cover, only 0.2% of bombs fell within 1,000 ft of the aiming point, even through 4/10 cloud only 4.4% were within 1,000 ft.
Military or the industries are seldom found in city centres you know.. quite typically they are concentrated on the edge of town, in well identifiable areas. This has a reason of it's own, you see, most European cities are very old. Originally none of them had industries, but a small medieval core or center. Industrial areas were built up at the edge of this core as there was plenty of space at the beginning of the century.
The medieval core of a European city is typically very small. If you look at Hamburg as an example, in 1600 it had a population of 40,000. In 1800, as industrialisation was getting under way, it was 130,000, by 1870 that had risen to 240,000. In 1939 the population was more than 1,700,000.
Cologne had 40,000 people in 1600, 145,000 in 1880, 767,000 in 1939.
The medieval core was very small. As the industrial revolution got underway, factories were built on the outskirts of the town, people moved in to houses around the factory and the town enlarged. But that didn't happen in one go. Factories and housing were added bit by bit, largely unplanned. Large European cities consisted mostly of mixed industrial, commercial and residential areas.