Of course, were one to plug the miniscule chance of terrorists entering through Canada, they would presumably seek other ways to enter the USA, just as going through Mexico or - the easiest way, really - simply flying in to a US airport.
Erecting more border security with Canada would, therefore, probably have the effect of costing a great deal of money without actually reducing the likelihood of terrorism at all.
The United States simply cannot prevent terrorists from entering the USA with fences and guard dogs. It cannot be practically done, not for twenty billion dollars, unless the USA wants to become a backwards hermit kingdom a la North Korea. Terrorism prevention doesn’t start or end by calling a fence company.
If beefing up border checkpoints would cost extra money, then presumably reducing or removing border checkpoints would save money, possibly millions of dollars, that could then be spent on increasing cross-border law enforcement cooperation and swift investigation of alleged terrorists.
An open border would also likely improve the economy of both countries as companies will find it easier to do business across the border and tourists will be more likely to take international trips. That will do two things - one, it will increase jobs, providing more employment and/or better employment. Two, it will increase cultural understanding and contact. More Americans than ever will be able to hop up to Quebec for a day or two to understand what it feels like to survive in a mostly non-English-speaking society. Both of those things (jobs and cultural understanding) work against radicalization. Which would you rather have, a prison full of terrorists or a town with neighbors who never became terrorists because they were able to get a job and feel comfortable and accepted in their neighborhood and region?
Hopefully the statue of limitations is past, so I can admit to having gotten lost driving in that area, in the 1990’s, and to being temporarily unsure what country I was in. The rule was that after entering the US, you had a responsibility to drive into an office in the center of the town to check in. Now things are much tighter, and taxpayers are on the hook for it:
Similar examples can be found along the border between Port Roberts Washington and Delta British Columbia, where you have to go through a border control to take your child to the nearest playground.
The further back in time you go, the border formalities were less and less; before the US Border Patrol was established in 1924, I think there were none.
There are economic costs, and it’s darn inconvenient for people in the area. And, because of the rather similar per capita incomes of the two countries, there’s virtually no compensating benefit.
The border probably also causes some deaths when the nearest trauma center or fire station is in the other country.
Why? Because Canada is worried about guns being smuggled in from the US? If so, it wouldn’t justify the US having an incoming border control.
Here’s an example of the horrors which used to occur back when that border was essentially open: