The left has tried to frame it as if it's a border wall vs. everything else as if funding a border wall means all other enforcement methods will go away. It's ridiculous. They keep repeating that a border wall won't stop all immigration. It's not supposed to. It's just one important piece of the pie.
Possibly some people in the left have framed it that way. My general understanding is that the MAIN argument is that the money proposed for a border wall would be spent more
effectively elsewhere, whether in alternative means of border security OR in other areas that would benefit the US economy and security more.
Please visit the following short summary of points against extending the wall.
https://www.americanimmigrationcouncil.org/research/cost-of-border-wallA study was done on the actual effects of building 548 miles of walls along the US-Mexico border following the Secure Fence Act of 2006.
"
1.Did the Secure Fence Act lead to a change in migration patterns?Yes, but the effect was small. Using a unique dataset that contains information on the
origin and destination of (primarily unauthorized) Mexican migrants, we document
that migration fell between Mexican municipalities and U.S. counties that were more
affected by the wall (i.e. by geographical proximity). The magnitude of the effects
suggests that the direct effect of the wall expansion was to reduce migration flows
by 0.8%. The direct effect, however, does not account for other effects, such as
whether migrants changed where they migrated to or whether wages changed in the
destination. To account for these, we develop and estimate a general equilibrium
spatial model. We find the total effect of the wall expansion was to reduce the
number of Mexican citizens living in the United States by 0.6%, or roughly 82,650
people.
2.What impact did the Secure Fence Act have on the U.S. economy?The effect of the Secure Fence Act on the U.S. economy – after accounting for changes
in wages, the cost of goods, and the internal migration of U.S. workers – was largely
negative. College-educated U.S. workers lost an equivalent of $4.35 in annual income,
while less-educated U.S. workers benefited on average by only 36 cents. This number
is less than the $7 per person construction cost of the wall.
3.What impact did the Secure Fence Act have on the Mexican economy?The Secure Fence Act on the Mexican economy was negative. College-educated
Mexican workers lost an equivalent of $2.99 in annual income, while less-educated
Mexican workers lost on average by $1.34 per year."
https://cpb-us-e1.wpmucdn.com/sites.dartmouth.edu/dist/d/2043/files/2018/11/ADM-Border-Walls-Executive-Summary-1kguush.pdf