From what I've read, that is not the case.
If you are USA Citizen and you are crossing the border without documentation, then you can call others to come with the required documentation, You get detained in the mean time.
If you are not a USA citizen and you are trying to get in, they will deny you access. But if you claim asylum then you need to fill out an asylum claim form, you then get detained for a couple of weeks or so, you then get interviewed then back into detention. Weeks later if the assessor doesn't think you have a valid claim you are then denied access, if you are assessed as having a valid claim then you are back in detention center to await the judge ruling. 'You might want to make a claim for parole, if not just stay in detention. If detention takes several months, then you might get let in on parole, to await your court case.
If you don't turn up to the court case or if you are denied assylum then you become an illegal immigrant and will then face deportation. If you try to remain, you will be on the run from the law, working without a tax number, working on cash jobs only.
It is much easier for them if they get granted asylum, then they can get tax number, they can get appropriate jobs, schools can vote, get medical care etc.
Here is a decent article talking about the differences in immigration/asylum policies between the Trump and Biden administrations.
President Biden promised a more humane approach but his border policy has been sharply criticised too.
www.bbc.com
It talks about Title 42 expiring (was an emergency policy just for the Covid pandemic
It talks about the Remain in Mexico policy that Trump's administration put in place but that Biden's administration got rid of.
It talks about the "Zero tolerance" policy that Trump's administration put in place but that Biden's administration got rid of.
Which of these are you bothered about?