"the swiss equivalent"

As OP explains, freedom of movement can't be stopped in isolation from the rest of the bilaterals.

(btw funnily Schengen is just about the border control, we're talking about freedom of movement which is a different thing, e.g. UK wasn't in Schengen but the freedom of movement applied to UK as well before brexit, tho I guess people use Schengen interchangeably)

Which immediately triggers the guillotine clause in all other bilateral treaties including movement of goods and services, Horizon, energy market etc.

„Exiting the EU“ is a perfectly adequate way to summarize it to a world audience that doesn’t care about the details.

Even worse then - no more visa free travel, and no more international collaboration on crime. I must wonder, who would profit from these?