The EU chose to not make solutions available and stuck it into a "take it or leave it" basket.
So I'm really curious: What, do you suggest, should the EU have offered?
You basically reiterate my point, that it is "take it all or leave it".
The first step to a solution is obvious right from your phrasing: Put it up for a negotiation. Stop viewing this as "take it all or leave it".
Or, alternatively, be ready to deal with "leave it" as an option. Which, I'd observe, the EU legally was, as this is a legal option that has always existed and is now occurring with no bloodshed, which as these things go is still a well-above-average accomplishment. But psychologically the EU was clearly not ready for this; the expectation is still clearly that, like the United States, members may join but not leave.
That’s like saying we should put the right to live up for negotiation, as humans don’t need to live anyway.
If you allow free trade without free movement, companies can move all jobs to another country, and your country might end up with no jobs, and all people poor and fucked.
The only way to guarantee fairness in trade is if your citizen can move to wherever the jobs are, too.
This is a constitutional cornerstone of the EU.
The EU has no ontological right to exist. It is not an immutable fact of the universe. It is not rationally or logically valid to reason from "The EU requires this attribute for it to exist as I envision it" to "This attribute must be attainable at a reasonable price." or any variant on that.
I take a historical view on these things. Things are always changing. There exists no polity in history that only grew and never shrank, excepting only those polities that are new enough to not have shrunk yet.
I'm actually sort of becoming something of a secessionist. Not pro-Brexit or pro-Calexit or pro-any-particular-secession, but just generally in favor of the idea that since polities are inevitably going to shrink at some point in the future, it is preferable to make sure that such processes are as easy and as bloodless as possible. People shouldn't need to die by the thousands or millions for something so predictable. I am coming to believe it is a mistake to ever think that one can "permanently" bind a smaller polity into a larger one. And I believe the US has the much greater problem here! The US has no established mechanism for leaving (though a Constitutional amendment could make it possible), and a big ol' Civil War that says it's not possible in the bloodiest possible way. To the extent that we are having similar issues arise in the US, we have no peaceful mechanism for dealing with it.
The north of my island, Ireland, is a particularly interesting question, independent of Scotland, pardon the pun. Certain breeds of criminals get very fat on smuggling.