I'm not sure you're here for a reasoned discussion if we're already into "propaganda" and "phoney" but okay - would you be satisfied with 1997 levels of immigration and a government which worked towards that, or would that still be too much? And which specific categories of the Immigration Rules* would you abolish? I would guess you'd want all family migration abolished, which could be done by statute albeit there would have to be some sort of safety net for exceptional circumstances. But that then leaves students and workers which are the greater numbers by far. Fretting about small boats and families really is fiddling while Rome burns.
I would tend to agree that university education should be restricted to the academically elite. I think we would then have a struggle on our hands as to how to ensure that what we don't end up with is university education being restricted to the financially elite. I would also agree that students should be scrutinised if they claim asylum after being in the UK for some time - but they already are, by operation of s.8 of the Asylum and Immigration (Treatment of Claimants, etc) Act 2004 which requires a decision maker to treat their credibility adversely as a consequence of their late claim. Did you know that? I'm pretty sure you didn't know that.
And I'm sure that anyone who genuinely cares about asylum would also say that a teenager who comes to the UK as a student and realises that they are gay, or converts to Christianity, or whose country suddenly descends into civil war while they're here studying, shouldn't be prohibited from claiming.
I didn't list any jobs. I listed, very generically, the groups contained within the Immigration Rules, which relate to legal migration.
If you want to look at specific jobs, then you need to know that the "shortage occupations" are mostly very highly skilled. There's a lot of media focus on low-skilled fruit pickers and care workers, and it's right to say that if we really wanted those jobs filled by locals or let go if they can't be filled by locals, then it could be done, although fruit would then be extortionately expensive, and care would be hugely restricted and would have to be done largely by families - with the biggest impact on women, which then affects women's participation in the workforce as well as the way women are viewed by society in general. It would be regressive. But yes, it could be done, as long as you don't mind too much about that.
What I think could probably not be done would be for the UK to remain competitive in research academia, or technology, or science, or banking. And my view is that if we were to abolish those then we would sink into a huge recession which would be irrecoverable. When you talk about training our own benefits-dependent population to do this work I am not sure that you have the shortage occupation list in mind at all. Because Disaffected Dave** is probably not going to be a chemical scientist (shortage list, occupation code 2111), or a biochemist (2112), hydrogeologist (2113), civil engineer (2121), programmer (2136), vet (2216), actuary (2425), architect (2431), principal orchestral musician (3415), high integrity pipe welder (5215), and I can't be arsed with the rest of them but it's a very very long list of things that Disaffected Dave is eminently unqualified to do. Getting him into work is indeed a priority for any government but imagining that the Disaffected Daves of the world can "just" be trained up to meet all of the shortage occupations currently met by migration is magical thinking.
*not black letter law but a statement of the Secretary of State's policy at any one time, but for the purposes of these discussions, it counts as law
**sorry to all Daves, your name was chosen for alliterative convenience