No, it isn't. This is, in fact, precisely part of the point I'm trying to make here. People who live near the border don't have any inherent special knowledge about immigration policy and how to prevent illegal border crossings, and border protection staff don't have any inherent special knowledge about how to balance the need for preventing illegal border crossings against the myriad other needs that our government has, even in the narrow sphere of immigration policy.
Sure, a border wall will certainly stop a few crossings. A border wall also will cost an exorbitant amount of money--even the administration's conservative sum is 5.7 billion for one seventh of the wall, and given how cost estimates for the wall have been raised almost every time they're created and how government projects almost inevitably run over-budget this is almost certainly only going to be a fraction of the actual sum. A border wall also has to contend with the rough terrain that stretches across much of the border which will even further increase costs, a fact which the current administration is steadfastly trying to ignore. It has to deal with the fact that a good section of it runs through the Tohono O'odham reservation, which has refused to allow construction of the wall on its territory. It has to account for how a wall will affect animal migratory patterns that may affect environmental treaties the US has signed, how it could damage US-Mexico relations in a time when most illegal immigration to the US comes from Central America through Mexico for which US-Mexico cooperation is absolutely necessary to find a solution to, how it will affect the US' public image that may influence whether or not future legal immigrants wish to come to the United States, and so forth. These are all controls that Border Patrol, alone, cannot manage.
The Republican Party used to be the party of sober, responsible government, and used to be against expansive, theatrical government projects promoted by impulsive populists which come with massive price tag that can't even remotely justify it's meager efficacy just like this one. If the IRS asked for billions upon billions of dollars to massively expand their auditing infrastructure in a way that would only marginally increase the actual efficacy of tax enforcement at the cost of damaging many of America's other interests as well, we would say no. Why should it be any different here?