My understanding is during WW2 in the Pacific Theater that an island would be heavily bombed for a few days prior to invasion. However, the bombing was largely ineffective for eliminating ground forces since the Japanese had underground bunkers that were insulated from bombing. Similarly, in Vietnam underground tunnels and bunkers were leveraged. Also, during the Vietnam War bombing served as an early notice that American ground troops would be air-lifted to the area following the bombing event. The Vietnamese could then decided whether to attack or evacuate those areas if they so desired. They could pick their battles.
Clearly bombing is very effective in destroying strategic targets-- like in the European theater, mainland Japan, etc.. But, the military forces in Vietnam could not be destroyed out from arial bombing. It seems like an ineffective strategy.
Why was bombing pursued as a strategy?
In the context of the Cold War, the US couldn't pursue a ground invasion of North Vietnam because such actions could draw communist China into the war. It was thought that a sustained aerial bombardment of North Vietnam would be used to boost South Vietnam's sagging morale; to convince the North Vietnamese to stop supporting the communist regime; to destroy its transportation links, air defences and industrial base; and to stem the flow of men and supplies to the NVA and Viet Cong in South Vietnam.
When Operation Rolling Thunder began in 1965, there was still the belief in the American public and military command that it would be a short war. General Westmoreland was initially confident that the war would be over by 1967. During the first bombing, six US aircraft were shot down, shocking the Americans. They didn't realize that both China and Russia were supplying North Vietnam with advanced surface-to-air and air-to-air weapons. This was to be a sign of things to come.
President Johnson and Secretary of Defense Robert McNamara, cognizant of avoiding actions that might antagonize China or Russia, kept tight control over the campaign. There was little consultation between Johnson and the military leadership during the target selection process. Strangely, airfields in North Vietnam were off-limits, as well as the port of Haiphong and Hanoi itself. This infuriated the American commanders, pro-war factions in Congress and even some within the Johnson administration.
In April 1965, 3,500 Marines had arrived at Da Nang Air Base, marking an escalation of combat operations on the ground. Priorities changed, and the aerial campaign became secondary to the needs to the ground war and strategy. By Christmas Eve 1965, the US had lost 170 aircraft. The bombings didn't achieve its intended purpose, which was to end the war quickly without the need of substantial ground forces. The US had half a million military personnel in Vietnam by 1968.
The NVA and Viet Cong had an elaborate underground tunnel network: self-sufficient bases of operation complete with command areas, armouries, living quarters, supply caches, infirmaries and multiple access points. If part of the network was destroyed during the bombings, they would simply rebuild it elsewhere. The US couldn't shut down the Ho Chi Minh Trail, the jungle supply chain that ran from North Vietnam, through Laos and Cambodia into South Vietnam.
Rolling Thunder also exposed weaknesses within the USAF at the time. The chain of command was unnecessarily convoluted in Vietnam. Its aircraft and pilots, geared to fight Soviets in a nuclear confrontation, were ill-prepared for fighting a conventional war. This was exacerbated by the Pentagon's one-year rotation policy in Southeast Asia. While the first wave were well-trained, the length of the campaign meant that a gap in experience in its air crews soon developed.
By 1967, McNamara and others in the administration were convinced that both the ground and air war in Vietnam were ineffective. Hearings on the bombing campaign began in August on Capitol Hill, with both the military and the hawks in Congress intent on blaming the lack of progress in Vietnam on the limits the administration imposed on the bombings. McNamara, instead of playing the role of the civilian scapegoat, deftly rebutted their charges and admitted openly that Rolling Thunder by itself could not win the war, short of annihilating North Vietnam and its people.
With the 1968 presidential election looming, Johnson announced in March that bombings would cease north of the 19th parallel and would order a complete halt to bombing in North Vietnam on November 1. Hanoi, which had long rejected all peace talks while the bombings continued, agreed to talks with the US in Paris. Johnson would later decide not to run for a second term, burdened with domestic defeats, growing public resistance to the war and a Democratic Party split into pro- and anti-war factions.
The CIA estimated the the bombings caused $500M in damage to North Vietnam, with 28,000 military and 48,000 civilian deaths. The "Vietnamization" of the war would begin under the Nixon administration. The South Vietnamese took on a heavier role in the war, while the US tried to extract itself -- politically and militarily -- from it.