If you cannot control illegal immigration then you cannot control entry either.

Net immigration is falling. You can speculate why, and you can speculate when if ever that will reverse, but it is the present fact. You rule out, it seems, compulsory birth control (despite the fact that you several times refer to children of immigrants), so that makes it plain that the only thing you want to stop is immigration.

What do you mean that "most countries do manage better control of their borders"?
1. That fewer people arrive without going through immigration control at all?
2. That they receive fewer asylum applications?
3. That they reject more asylum applications?
4. That they do it faster?
5. That they more promptly or successfully deport failed asylum seekers?
6. That they are more effective at hunting down and deporting category 1 arrivals?

You say you want fewer immigrants. How do you plan to achieve that?