I think there is a lot of ranting going on about this that is unjustified. It's a bad situation for sure. The government at the time didn't keep records it should have known were important. The immigrants failed to ensure they had paperwork to cover their, and their kids, situation.
People in government/civil service failed to spot the importance and potential issues for the whole period since then. And those in government/social services/etc. didn't seem to catch on there was an issue for much longer than they ought but believed everyone without documented evidence was clearly an illegal immigrant. Probably a further system failure.
But none of it it malicious nor particularly failure to do the job, it was all a genuine flaw that emerged over time and that no one spotted for ages. The problem has been identified, admitted to, and steps are being taken to correct. No one is perfect, unfortunate things do occur. Let's just stop yelling about how awful this person and that person and everyone is, get it fixed, and move on.