that eliminates most of the danger and chaos because people will use the easiest reasonable method. An orderly process is much better, but orderly doesn't mean there needs to be a high barrier - the lower the barrier the easier to make it orderly.

Then, eliminate most of the public welfare services you identify. If there are jobs and other reasons people want to come, they will come. If the opportunities here are not better than elsewhere, the flow of people will be elsewhere.

Obviously it's a process to get there from here - but that should be the end goal. Less restrictions, less regulation, less government benefits - allow people to seek the lives they want to seek without a lot of government tipping the scales one way or the other.