Yes, closing the trails completely from the air is impossible.
However, the trails only worked because there were goods in NV to be transported via those trails. It made far more sense, and would be far safer, and more effective, to try to destroy the supplies BEFORE they left a factory in NV or arrived in NV. As others have noted, we COULD have blockaded NV, mined or destroyed its ports, etc. and we COULD have much more severely destroyed their rail and road infrastructure.
If those things were done, there would be little, if anything available for the VC to send along those trails.
So, the VC in the field would be far less well equipped and could be defeated far more easily. Further, the NVA would never be able to mount an actual ground campaign, which is what ultimately ended the war.
China and Vietnam share an 800 mile Land Border so bombing and blockading the harbours will slow down the supplied from the Soviet Union, which means either the supplies have to come through China which could be dicey given Sino-Soviet relations, or, Vietnam becomes more dependent on Chinese support. This opens up a potential issue of the the US regular forces, or CIA paramilitary forces going too far and attacking a shipment from China, while it's still in China...
I'll leave you to extrapolate the consequences.
As for transport through Vietnam to the warzone, a lack of rail would slow things down in the short term, same with taking out bridges. But long term, they just find another way to shift supplies and before long you're back to normal. This is why the trails were so effective.
The NVA Regulars would probably suffer for a short while, the VC on the other hand, far less so. I think the continued US presence would delay the ground offensive, an increased air campaign would delay it further, but I don't think it will cancel it, and ultimately, I believe the end result will be the same.
There are a couple of side issues that could turn things bad for the Americans, or at least turn them worse than OTL.
The more aircraft that are in the air over North Vietnam, the more are going to be lost.
The causes will be the same - Enemy fighters, AAA, Accidents, mechanical failure, the ratios may not be the same and may not match up to the increase in aircraft. However each of these need to be replaced. US losses OTL were roughly 0.4 Aircraft per thousand sorties, a huge reduction compared to WWII where it was over 9 per thousand sorties. The chances of getting back to WWII levels are ASB, however Korea was around 2 per 1000, and that is achievable, means rather than around 6,000 combat losses of fixed wing aircraft, you're looking at 30,000 with the resultant losses of crew at the same ratio.
All of which need to be replaced.
There's also the expense. Both sides will see an exponential increase in expenditure. The US are likely to have to pay for far more facilities, airfields, storage bases, support facilities, accommodation etc.
The more facilities you have, the more targets you present to the enemy. The more opportunities you supply as well. You provide opportunities for infiltration, theft and sabotage. You could mitigate this to some extent by not employing any Vietnamese civilians, but then you alienate the very people you're trying to liberate and become no better than the French, and drive more recruits into the arms of the VC. Just as bad, possibly worse is if you employ Vietnamese civilians but keep them sequestered from their families or keep them on base, effectively like prisoners, again you make them ripe for recruitment. Between that and the, as described above, "Toxic" South Vietnamese governments, and things really don't bode well for the US efforts.
In a war situation you tend to spend first and account later, but this could have some serious effects on the US Economy, and that's before you take into account the losses to the economy for supplying all that extra man power. Using the very very rough figures above, you're looking to replace 30,000 very expensive to train aircrew in various trades. You then have to replace the lost air frames, repair the damaged ones, rehabilitate the physically and mentally injured crews, replace the killed, incapacitated and captured crews, the financial bill is rising exponentially. The US will worry about how much this costs, the effects on their economy, the effects on their respectability.
The various flavours of Communists running North Vietnam won't be interested in the cost, the dialectic states that the proletariat will bear any burden to free themselves and cause the inevitable workers revolution etc etc.
The North Vietnamese on the other hand, to deal with the increased air presence just have to buy and site more AAA Guns and SAMs. And more POW space. All of these cost much less.
This ignores the domestic production. Depending on what and how they are producing, a lot can be done in small workshops, mostly modifications, same with repairs and upgrades.
The mass manufacture is likely to take place in China or the Soviet Union. Materially, I really don't think the North Vietnamese will lose out a great deal, probably the closest example that springs to mind is Germany from 1943 - despite the RAF and USAAF bombing Germany around the clock, industrial output rose year on year from what I remember.
I apologise for the mass of unstructured rambling, it won't be easy to follow. Short version: it's messier, takes longer, more people on both sides die, end result at best for the Americans is stalemate on the start line ala Korea, worst case, defeat.