Your idea isn’t a solution, it’s just you rambling something you heard on Fox and you regurgitated because you thought is was clever but it doesn’t address any of the issues here in a meaningful way.
Immigration is a federal issue and the authority to regulate it lies in the federal lawmakers hands. We can’t have an ad hoc policy for this situation. There would be no uniformity or predictability in process and outcomes.
Let’s say we did what you wanted, do you think every citizen is going to responsibly care for the asylum seekers? Do you think some would end up exploited or worse?
What about weeding out the bad actors, who will make judgments there?