Douglas MacArthur famously criticized the Truman administration for not permitting exactly this sort of more aggressive approach, and was relieved of command for it. He returned to the US amid massive acclaim as a war hero, and for a while his version of the facts dominated the popular consciousness. In order to cool down popular opinion and neutralize MacArthur as a political threat, the Senate held hearings on MacArthur's claims that the war was being mismanaged, chaired by the powerful leader of the Southern caucus, Richard Russell.

Among Russell's main purposes was to grill MacArthur on the shaky, untested, risky assumptions that his theory relied on. So MacArthur was asked questions like:

• You've suggested that land fighting in China could be handled by Nationalist Chinese troops on Taiwan. How many of those would you say there are? Could they sustain themselves in a ground war in China without need for costly American support?

• What would happen to Taiwan itself if the Nationalist army were to land in China and then be wiped out? Would the US then be obligated to defend Taiwan?

• You've claimed that if the Chinese were pushed out of the Korean peninsula they would sue for peace. What if they didn't? Would US forces then face a choice between invading Chinese soil to try and knock China out of the war, or else watch China amass another huge force across the Yalu River, ready to invade Korea again?

• If US troops were drawn into a land conflict in China, what would happen if the USSR seized the opportunity to attack Japan? If the US Navy were committed to supporting such a conflict, what if the USSR used submarine forces to indirectly attack Japan?

• Could MacArthur guarantee that the USSR, if it perceived that the US was distracted in China or that, if Communist China were in danger of collapse, it had an advantage that was slipping away, would not launch a ground invasion or a nuclear war in Europe? Would the US be ready to fight such a war? Would Europe? How many bombs did the USSR have?

I recognize you're focusing on bombing specifically, but the point was that any decision to escalate the war was fraught with risks in light of the nature of China as a belligerent (e.g. very large and incredibly difficult to invade, resilient, determined, backed by the USSR) and the overall strategic context (e.g. other US commitments to defend Japan and Western Europe). And as these kinds of questions should illustrate, there's not a neat distinction between escalating the war with strategic bombing and invading China; it couldn't be taken for granted that the US could attempt a strategic bombing program without consequences that might lead to a land war. Moreover, the above questions weren't idle second-guessing by politicians motivated only by self-interest: these were difficult and valid questions that MacArthur had a hard time answering. Faced with difficulties like these, the Truman administration calculated that the benefits of escalating the war by subjecting China to strategic bombing didn't outweigh the risks.

Source: Master of the Senate by Robert Caro, p. 372-381.