Both of these are wrong.

Non-EU means it's harder to get a permit, especially without working experience, but it's not impossible either.

Housing is difficult in cities like Zurich but calling it impossible is stretching it, especially if one is fine with a longer commute.

You can get housing, you have to trade money for time and commute with the (frequent and reliable) public transportation.

Meanwhile the parlement and the anti+immigration far-right vote all the time to increase landlord rights and margins. Most of them are landlords, of course...