I think it might be worthwhile to take a look at the US borders just to get an idea of what might be needed to secure them.
First some basics. The US border with Mexico stretches almost 2000 miles. Of that a few hundred miles are in urban areas but the vast majority is rural farmlands and deserts. Access parallel to the border is mostly non-existent or unpaved roads. There is also a large Native American Reservation that exists on both sides of the border and where the US has no authority to build any wall or even monitor traffic between the part of the reservation north or south of the border.
Then there is the Gulf Coast. That border is at least 1600 miles long and again, most of that is not urban and there is no border access road. There are also lots of rivers running into the interior of the US with no border controls at all.
Next the Atlantic Coat. It's over 2000 miles long and as with the Gulf Coast there are lots of bays and rivers allowing direct access to the interior of the US.
Our border with Canada is really two borders, about 4000 miles between the 48 states and another 1500 miles between the US and Alaska. In some areas border control is as detailed as a black line drawn on the floor of a reading room in a library. Tables on one side of the room are in the US, the other tables in Canada. There are also a half dozen or so unstaffed crossing points as well as the miles and miles of virtually unmonitored border.
US West Coast has a border of over 2000 miles while there is an additional 6000+ miles of Alaska Pacific coastline.
Now lets move on to the "Wall". One fact of life is that it will always be cheaper to build ladders to scale a wall then to build and maintain the wall itself. It will often be cheaper to tunnel under the wall than to build and maintain the wall itself.
So a wall itself offers very little security. For security we would need eyes on the borders as well as the infrastructure and technologies to respond rapidly to incursions. To intercept people crossing one of our borders without going through the monitored checkpoints requires that we be aware of the incursion and have the capability of intercepting the individuals before they can disappear into the general population.
If we have eyes on the border and the ability to respond in time to incursions then there is no need for the wall.
BUT... What would be the cost of having the ability to have eyes on the borders and the technology and infrastructure to respond in time to stop incursions?
Didn't you guys also recently reduce the requirements of a Visa for folk coming from Mexico so now all they need is their Mexican Passport and the eTA (electronic Travel Authorization that cost $7CAD and can be done online)?
The US has had a policy of extreme vetting for anyone trying to legally enter the US for many, many years.
I mean, I was extremely vetted for my first 10 year US entry visa. Political affiliations, addresses for 10 years before that, police records, tax returns, health checks; all checked, etc. etc. So, I could enter and leave the US for 10 years.
After that one expired, the second one was similar. This time a biogeneticwhatever profile also needed to be obtained. On pupils and stuff like that.
Those visas weren't fun to obtain; I got extremely vetted. Political affiliations, addresses for 10 years before that, police records, tax returns, health checks, pupils, etc. etc. etc.