I presume you can't work or claim benefits either without some sort of ID.
That's supposed to be the case in the UK too. But as usual, the authorities (i.e. border force, HMRC, police, etc) aren't remotely interested and need a rocket up their arse before they do any policing of those laws when it comes to the black economy as such employers don't give a toss about such laws, they're "under the radar" often not even registered for tax/nic, pay cash in hand, ignore NMW laws, etc., so aren't bothered about the legality status of their employees. HMRC don't know about them (can't be bothered to look), police only care if someone gets seriously injured or dies, etc.
In the meantime, hundreds of thousands of genuine small businesses are trying their utmost to comply with the law, check passports, pay tax/nic, pay NMW, etc., yet HMRC come down on them like a ton of bricks for minor infringements.
As always, the authorities only go after the soft/easy targets to make themselves look good. Fast food places where "staff" are virtually treated as slaves living in squalor above the shop are left alone because they're in the "too hard" pile on the authority's desks!
Whilst I'm in favour of ID cards, I think the argument is pointless until we start enforcing the laws we already have and stop with the authorities being too lazy or too scared to deal with the real criminals operating the black economy!