It's not even a case of wanting to leave "home".
Relocating in search of work is exactly what the government tell people they are supposed to do. And the young who aren't yet restricted by a spouse's job or DC in school or needing suitable accommodation with a baby, are in the people in best position to do this.
Except they can't any more, unless they already have a job - and one with sufficient hours - when they get there. This isn't restricting young people's options to shared houses: it's removing their accommodation completely.
Before anyone says, Ooh, they used to manage in the Olden Days: did you realise that in the Olden Days employers often used to provide accommodation to go with the job? Everything from hostels to whole housing estates (I'm not just talking the chocolate box ones). There were people who cycled from Scotland to Corby - but had a hostel to sleep in when they got there, while they got set up.