Bit lost here. Which of nn's posts is a logical outcome of which others?
Over half of the total number of immigrants come from non-EU countries. The UK has always had total control of the number of immigrants from those countries, but we haven't, because we need the people.
People wouldn't need to be taxed to extinction. Immigrants are not a homogenous group. Many of them are highly skilled, filling skills gaps, paying taxes and contributing towards products whioh are then exported. The UK earns billions from foreign students, which is why Hammond wanted to exclude them from immigration caps.
Other immigrants are doing low paid work, often below their skill level, because the UK has an ageing population and needs younger people to support society and the economy. And so it goes on....
The government(s) should never have made empty promises to bring the net immigration figure down to below 100,000, because it was never going to happen and it won't in the foreseeable future. There are far more than 100,000 immigrants from non-EU countries, despite the tightening of eligibility criteris. There are over 30,000 immigrants from Ireland alone, eligible since an agreement from the 1920s. It would be a very foolish government which tried to change that.
Even with Brexit, it's highly unlikely that immigration could ever be brought down to the kind of figure people have been promised, unless there's a total collapse of the economy and I don't suppose many people want that.