That isn’t actually true, sort of misses the boat on who the USA was actually fighting, and in a way actually circumvents one of the more common “we coulda won the war” arguments, which I realize you’re not making but I may as well cut it off at the pass.
The United States was fighting against two distinct combatants; the North Vietnamese Army, who I’ll refer to as the NVA, and the Viet Cong, more properly called the People’s Liberation Armed Forces, hence PLAF for short. The former was a conventional armed forces, the latter more or less a guerrilla outfit, but a very large and reasonably well organized one.
OVer the course of time the Vietnam war seems to have become remembered as a fight against guerrillas. But actually the majority of the USA’s combat efforts, over the course of the war, ended up being against the North Vietnamese, and was fought as a conventional war, with set peice battles, jet fighters dogfighting, the whole nine yards. The escalation of U.S. involvement in South Vietnam resulted in an escalation of NVA involvement in South Vietnam. In fact the Viet Cong didn’t fare well against their American and South Vietnamese opponents, militarily speaking, but were propped up by the NVA (and, through them, the Soviets.)
The USA’s unwillingness to open the floodgates against North Vietnam directly was a rational response to the political reality of the situation; American intervention was justified on the basis of supporting the government of South Vietnam against the PLAF insurgency. North Vietnam had the opposite justification; they justified THEIR involvement by saying that they were supporting a popular movement against an illegitimate puppet regime. Both the USA and North Vietnam were fighting a proxy war through South Vietnam; the PLAF, as it happened, were caught up in it, but eventually took a military back seat to the NVA for the simple reason that disorganized militias usually get slaughted by regular armies, and the PLAF was no exception.
A full scale attack on North Vietnam may well have crippled, or destroyed, the NVA, and so the Vietnam War as it was being fought could have been “won.” As RTFirefly has pointed out, expansion of the war didn’t help matters and probably made things worse, but for shits and giggles let’s just assume that a full scale invasion of North Vietnam would have worked, and they would have “won.”
Of course, the Iraq War as it was being fought in March and April of 2003 was “won” too, in the sense that the Iraqi armed forces was destroyed. However, the USA would simply have been trading one problem for an even larger problem - occupation of the entire country, a loss of what popular support they had in South Vietnam, and an intensified insurgency on a grand scale (Vietnam is 75% the size of Iraq, but has three times the population.) International opposition to the USA’s involvement, which was already there, would have quintupled. It would have been about as fun as the Soviet invasion of Afghanistan, except against an enemy eight times larger.
The Vietnamese objective - which crossed to both sides of the border - was quite straightforward; Get the foreigners out so we can run our country. There was no state that could have existed involving American occupation of either or both sides of Vietnam that would have satisfied that objective, and so in one way or another the war would have continued unabated, likely with the enthusiastic support of China and the Soviet Union.
On top of that, an invasion and occupation of North Vietnam makes detente with China in 1973 almost certainly impossible. So in addition to fighting an endless war of occupation, the USA has two superpower enemies from 1973 on instead of one, who are continguous to Vietnam and can likely support the Vietnamese insurgency from now until the cows come home. How does that sound?
No victory was possible.