I lived in a house with my teenage daughter and that's another good analogy. Lots of shouting and slamming of doors because she didn't agree with or like things that were said to her. Then she moved out and now has a little family of her own, in her own house where she can do what she likes. And me and her mother, instead of being the people who were continually "ruining her life" (in her words) can meet her as adults and equals. From being a drama queen teenager she's now a calm and confident mum. And it was the same for me and my parents when I was that age.
My vision for our future relationship with the EU is a bit like that, as sovereign states that treat each other as equals, can trade together without throwing tariffs up and who can co-operate on selected policies and ideas if need be but who are free to diverge on fiscal, monetary, social policies and other rules and regulations. Pretty much the same relationship we have with the USA, China, Russia, India, the UAE, Saudi, Vietnam, Canada, Australia and a host of other sovereign nations. We don't always see eye-to-eye with these countries but in general we live and let live, trade happens and the world carries on turning.
Schengen was a European initiative, between 6 countries originally, not an EU one, The EU absorbed it as part of the Amsterdam treaty. There's no bar to us having some sort of freer movement with selected countries if that's what we want. There's no bar to us having an alternative to Erasmus, which involves European universities as well as those in the US or other non-EU countries.
I could travel to Europe (& did) when I was a youngster, long before Schengen, Some of my contemporaries spent a year at foreign universities in the 1970's. My son went to university in the US, which took some paperwork and the hssle of getting a visa but plenty do it. And he was charged exactly the same as his fellow students who were locals. Migration will still happen, both ways, but might be more difficult. But then plenty of people retired to Spain or bought property there before Schrngen or the Lisbon and Maastricht treaties.
Life will go on, some things for the better, some for the worse. The world won't end because we're no longer an EU member. Whart it will look like in 5 years I couldn't say though and no one can. That's a fact.