Those people who have jobs lined up will still be able to move - as evidenced by the figures quoted for non-EU emigration.
The odds of getting a job 'lined up' in a country where you do not already have permission to live or work are vastly reduced, especially if you want something more secure than a temporary holiday job. For an overseas company to sponsor your visa, you need to justify the time, inconvenience and cost this involves, and answer implicitly, or actually prove in your application the question 'why you, and not one of the x million citizens who are here already and ready to start work?'.
Everyone has some specialist skill. Most people don't have the high level of provable specialist skill that encourages an overseas employer to spend thousands of pounds and wait months for their arrival. Yes, some counties offer points-based systems, or even encourage people in short-staffed professions to apply -- but it's disingenuous to cherry-pick those friendly-sounding set-ups. Across the board, the requirements can be and mostly are a lot harsher, restricting entry to those with high levels of education, money to invest, or who are in upper management. Those people in a position to 'line up' their international jobs are sounding an awful lot like the dreaded 'elites' we're all supposed to disdain so much. So, that's great. Post-Brexit, horizons for average UK citizen: curtailed. But the elites are still fine.
The bricklayer, the nurse -- no one in this level of job is getting a work visa to America. A large proportion of UK citizens who emigrate there do so because they have an American spouse or some other family claim to citizenship, not because a company has brought them over.
For a US company to bring in an international new-hire on an H visa costs about $5k; they must apply for you in April, and wait until October, and then there's a lottery because the H category is usually oversubscribed. You must have a university degree or 12 years' experience. Your dependents may not work. If you already work in one of their international offices and they want to transfer you on an L visa, you have to be employed at management level and have worked there for at least 3 years. If you want an O visa for exceptional talent, your applicant must provide proof that you've been nationally or internationally recognised, preferably with media clippings, references etc.
I know we're not just talking about America, but I list all this visa-related hoop-jumping (and I haven't even started on the fees! the embassy interviews! the biometrics!) because it's infuriating to see how people minimize what we're going to lose when our right to live and work in the EU disappears. Oh, it's not a big deal -- just line up a job elsewhere, and fill out the forms. In most cases, that's wishful thinking. We've greatly limited our own options and opportunities. If you want to explain how that's worth it, then go ahead, but don't pretend it's not a massive disadvantage.