Although one could consider the Blitz to be strategic bombing, the fact remains that the bombers used by Germany were mainly two-engine aircraft with smaller bomb payloads (He-111 carried 2000kg, a B-17 2700kg, the B-24 3600kg, and the B-29 9000kg).
Next, compared with the Allies, the Germans produced many fewer. Wiki gives about 6500 He-111, vs 19500 B-24s and 12000 B-17s. In addition, the British produced large numbers of 4-engine bombers. The B-29 program, coming later in the war, only produced a little less than 4000 units. On the British side, the Lancaster (more than 7000 built with 5000+kg load) and the Halifax (more than 6000, with 5900kg load) each exceeded the number and bomb capacity of German 'equivalents'.
Given the circumstances of the war, with Germany primarily involved in land-based operations on the continent, they prioritized aircraft in support of army operations. After the fall of France, the only way for the British and the Americans (once they entered) to attack Germany was with the heavy bombers. To do so, they produced a huge number of the bombers and then the fighters to support the bombers and eliminate the Luftwaffe as a fighting force.
Furthermore, Germany did not have the production capability to make heavy bombers in addition to everything else they needed. A review of the Wiki page on heavy bombers shows any number of proposals, but few models reached operations, and almost none as actual bombers, and none in any quantity approaching that of US and British models. Even at the height of the Blitz, the Germans were sending several hundreds of 2-engine bombers, while in 1944/5 the US and British routinely managed 1000+ heavy bomber raids.
As an indication of the financial costs of heavy bombers, the entire B-29 project cost on the same order as the Manhattan Project. Germany did not have the ability to do either one of them, unless they didn't do much of anything else.