They mostly only make the asylum claims after they’ve been caught, so I think we definitely need the wall.
But it all needs to be changed. Apparently Trump has had the power to stop main immigration draw all along, as the well-regarded former DoJ attorney Sidney Powell wrote in October last year, but he apparently doesn’t have the will to do so and instead is now talking bringing more in legally so they don’t have to bother with coming in illegally. It was a bad sign when he got Kushner and Pence involved—aye-aye-aye!
https://dailycaller.com/2018/10/22/immigrants-invaders-power-president/
They do make the claim after arrival, but if they had no hope of asylum (except in very rare circumstances) or being released in the US then they wouldn’t bother trying.
“Apparently Trump has had the power to stop main immigration draw all along... but he apparently doesn’t have the will to do so”
The legal argument that has been made, is that binding International Treaty require the USA to accept and provide due process to asylum seekers. Treaties take legal precedence over legislation, and require larger majorities to pass.