You can’t just get work visas, you need to already have a job, it has to be sponsored. And the logistical hoops needed to jump through to employ someone from the EU mean that the company doing it needs to know that it’s worth employing that person; it’ll take months to prepare (for both employer and employee), so it’s not really worth it unless that person has specialist skills. I’ve know a few people who’ve gone to work in the US; always for big companies who can afford errors (P&G, Pixar, Google), and because they have specialised, useful skills that outweighed the logistical issues.
And regarding degrees: a graduate with a good degree is probably relatively smart, it’s very easy to get references, they’re likely to be malleable and unlikely to have much baggage. Say the student is expected to get a first in CS (and the final year work is something interesting) from somewhere that signals well, like Oxford or Cambridge, companies will fall over themselves to offer jobs, regardless of the hoops needed to jump through to hire them, because it’s as close to a sure bet as you are going to get as an employer.
This vs. the EU, where if you have the language skills to work somewhere and are free to relocate, you can do that with no penalty; no visa needed, no nothing.