They need a meeting with an asylum officer and then the officer's supervisor has to sign off on it. That doesn't happen in 5 seconds. Then there is this:
If an alien is found not to have a credible fear of persecution or torture, the asylum officer shall provide the alien with a written notice of decision and issue the alien a record of the credible fear
determination, including copies of the asylum officer's notes, the summary of the material facts, and other materials upon which the
determination was based. The asylum officer shall inquire whether the alien wishes to have an
immigration judge review the negative decision, which shall include an opportunity for the alien to be heard and questioned by the
immigration judge as provided for under section 235(b)(1)(B)(iii)(III) of the
Act, using
Form I–869, Record of Negative Credible Fear Finding and Request for
Review by Immigration Judge. The alien shall indicate whether the alien desires such review on
Form I–869. A refusal or failure by the alien to make such indication shall be considered a request for review.
So now there is an asylum officer who has to take down the information and write up their response. Then the documentation is sent to a supervisor for review. Then, if denied, they are told it can go to a judge. How quickly do you think this happens?
But it all goes to the bigger point, if they ask for asylum this all kicks in and it doesn't matter if they are from Mexico or Venezuela. You have yet to find a section of code suggesting a difference. There are 2500 asylum officers in the US, if filled all the way which they aren't. You aren't capturing a person and having a hearing and a supervisor review and a judge hearing all in 5 minutes. Also, they are allowed to speak to anyone they wish, including a lawyer, before speaking with the asylum officer. That also delays things.
By the way, if your example was a person crossing from Canada you would have a point, it appears we do have exceptions in the law for people coming in from Canada.