That's true. And Biden recently issued an order saying that. Biden's asylum ban basically said that you can't come in for asylum unless you can prove that you sought out asylum elsewhere and were denied. It's a de facto end to arbitrary asylum seekers but you still have to process the application to deny it.
@Jack V Savage has the right of it. What do you do with the people while you are processing their applications? You're not letting them into the country legally but since the application review process takes a long time, many of them are illegally entering the country to make their claim since it's faster than waiting on the other side.
Unless the system for granting/denying asylum is made faster/smoother, the asylum seeker problem is never going to get better. But these are people seeking legal status through a federally created process...which is why they're so willing to get on buses and be sent to other parts of the country. They think they're going to get their applications processed there. If these were true illegals, who were trying to sneak in and live off the grid, the last thing they would do is get on government buses to unknown parts of the country.
A huge part of the public facing problem is that the issue is constantly being misrepresented and people are worked up but they don't understand what's happening.