It seems like, although the US forces were well equipped and trained, they never focussed on invading the North and, for example, taking their capital. Didn't refraining from launching ground attacks on the North allow North Vietnam to supply their forces in the South?
There are multiple facets for this.
The first one to consider is the geopolitical nature of Vietnam before the escalation of the war around 1964. By 1950 China is the first to establish diplomatic relations with Vietnam. Though it can be certainly argued that post-1949 China wanted to ideologically ally with its neighbor, there was also the pragmatic component of using North Vietnam as a buffer against South Vietnam. Within that same year the Chinese set up the Military Advisory Group, an organization that manages and sends over numerous quantities of munitions, food, and medicine to the border. Unsurprisingly the M.A.G also brought along trained Chinese personnel and anti-aircraft and artillery operators that trained the DRV (North Vietnamese) troops who would have a rather notable effect in 1954 with Dien Bien Phu. By 1958 the Chinese would move the M.A.G headquarters to Hanoi, establishing a closer link between the Chinese and the Vietnamese. Though the Soviets send help, much of the aid to North Vietnam until 1970 comes from China. Between 1956 and 1963 almost 320 Million Yuan of equipment in the form of food, ammunition, guns, artillery, aircraft, vehicles, and even consumer goods are poured into the DRV.
Now what does this mean for the US? By 1964 there was a sudden shift in the stance of China's advice for Vietnam. Prior to 1964 much of Chinese policy was to "clean house," build from within and take a route of caution to avoid open protracted conflict. Considering the aftermath of the Korean War and China's involvement, the Chinese policy of Caution post-Korean War makes a good amount of sense.
However by 1964 two things had happened. The Cultural Revolution began to sweep across China and the Sino-Soviet Split due to differences between Mao and Khrushchev grew to be irreconcilable by 1964. For the North Vietnamese this was a boon. China and the USSR would compete to court the DRV, a local Communist ally. Though this is a simplification, the radicalization of Chinese politics along with the spur of the far left's desire for sweeping revolution very well may have contributed to the huge movement and commitment of aid to Vietnam post-1964. Up until 1964, the Chinese stance though lavish with aid did not mean total protection.
This all however changes by August 2nd 1964, the day of the Tonkin Gulf Crisis. With the Tonkin Gulf, the US retaliation for DRV torpedoing of ships alerts and begins the Southern Chinese Armies to move into combat readiness. Soldiers and anti-aircraft units are moved into north Vietnam and the Chinese begin to build roads, railroads, and airports to create an infrastructure for moving troops into North Vietnam. By 1965 the official Chinese policy for responding to US action is one that can be summed up as, "not seeking confrontation, but not avoiding confrontation either."
Curiously, though Operation Rolling Thunder begins in 1965 it would not provoke the Chinese. However the US was warned that if United States troops crossed the 17th Parallel the Chinese forces in South Vietnam would mobilize. What is noticeable however is the massively growing Anti-Aircraft placements all across North Vietnam that begins a little bit prior to Rolling Thunder.
For the US the inclusion of China and an escalation of all out War between the two powers was undoubtedly a worrying prospect and one that risked an escalation of conventional war to nuclear war.
The second facet to consider is the nature of the South Vietnamese. By 1965, the South Vietnamese government was in short seriously in disarray. Having faced the assassination and coup of Ngo Dinh Diem in 1963, the brief ascension and then subsequent removal and disassembly of the the Junta Led by Doung Van Minh in 1964 and the longer but still brief rule of Nguyen Khanh until 1965 where the other commanders Ngyuen Cao Ky and Ngyuen Van Thieu removed Khanh. In other words between 1963 and 1965, the faith in the leadership of the South was thoroughly shaken and within the South, there was too much chaos and disarray due to the protesting buddhists, the disapproval of the regime changes, the split within Vietnamese politics between Diem-ists and Anti-Diem factions, and constant coup attempts.
In short though the South Vietnamese did have the backing of the United States, it was difficult to get a good foothold and mount a serious offensive due to how chaotic the mid 60s were for South Vietnam.
The third facet to consider is the domestic viewpoints of the Vietnam War. Though there was indeed hawkish US citizens especially from the Goldwater camp, Lyndon B. Johnson himself was very recalcitrant to commit to a full on invasion of Vietnam. Furthermore the international portrayal of Vietnam and US involvement especially after Rolling Thunder (at least for many of the orthodox school) was hardly positive. The overseas commitment at best was expensive.
There's a fourth facet, though this one is more of a recent find. Problems of espionage. Much of the difficulty of mounting a full invasion was the sheer amount of infiltration that occurred within the South. That is not to say that the Americans were inept at espionage (though certainly there are many..humorous accounts...), but that the North Vietnamese had a higher degree of success. Enough so that almost every large movement and offensive launched by the South and the US were anticipated. For the US it meant that the North was at times more prepared. That isn't to say that the US couldn't have fully committed, but war within Vietnam would have not only most likely provoked an open conflict with China, but also would have been anticipated and prepared for.
In short, The US couldn't have invaded even if they wanted to. It would've meant a war with China if it was in 1965 and if the US fully committed in 1972, the political clime would have been far too negative especially post-Tet Offensive to even attempt such a commitment.
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