How does this work? Are people just routinely evicted when the rate goes up and they can't afford the payment anymore, or is there some reason this doesn't happen?

From my US perspective, I would rather rent forever than risk such a loan, so I suppose there must be something else at play which makes your approach less awful than it would be if we did that here.

Adjustable Rate Mortgages destroyed a lot of people’s wealth in the US back in the housing bubble. I don’t know if the laws are supportive of borrowers in the UK, but in the States ARMs have a bad reputation that they probably won’t shed for 2-3 generations.