First off, none of us are absolute dictators who can just impose our will on a country, nor are any of us founding a new country.
But there is another option you didn't list: perhaps a country, through the democratic process, decides it just
doesn't want any more immigrants for a while. No more "nonimmigrant" visas like H1-B (that mysteriously turn into permanent residency eventually), no more "diversity lotteries", no more "temporary protected status" that lasts decades and results in lawsuits to keep it when the "temporary" status is taken away.
Is that an acceptable choice?
To me, a good system looks like this:
We accept a reasonable share of the world's refugees and screen them carefully
I would be fine with taking refugees from Mexico and Canada. There has, so far, not been a reason for any refugees to come from those places.
I do not see why the U.S. needs to somehow accept refugees from around the globe when there are other safe countries such refugees are closer to.
The rules are clear and applied consistently
I believe this is how it currently works?
Immigration courts are fully funded so people get timely, fair hearings
Immigration courts are fully funded, and are funded primarily independently via user fees.
It can often to be an applicant's benefit for a hearing to take a very long time, such as appealing an order of removal for someone who entered on TPS, for example, or appealing a denied asylum claim. I would agree it would be better if such hearings were heard quickly, but you should acknowledge that a common legal strategy is to try to stretch it out as long as possible since that makes it easier to stay in the U.S. a lot longer and possibly secure some other way to stay.
Legal status isn’t taken away arbitrarily or for political reasons
I am not aware of that happening either.
Removals, when they happen, are humane,
The best way for that to happen is for people who enter without inspection or who overstay to leave voluntarily.
keep families together when possible,
Yes. Families can be deported together, for example. Having a "U.S. citizen child" does not grant a visa to the parents, who have a "U.S. citizen child" merely because they gave birth in America. They should be repatriated together, but do consider that DHS often has a difficult job to do due to so many children born out of wedlock.
and help people plan where they’ll go
I don't think it's the U.S. government's responsibility to help other people with their travel plans. Perhaps they can plan for their own where they'll go. After all, they figured out how to enter the U.S. - they can probably figure out how to enter to a place that they have a legal right to reside.