Yes and housing not included in inflation numbers.
If someone works 1 hour in some form they're not included in the unemployment numbers ! Imagine the real unemployment/underemployment rate also allowing for all those 'hidden' in various Govt. training/retraining schemes etc.
Government and Corporates are also beneficiaries of low numbers in various ways eg politically, wages pressure, welfare payments to name a few.
A couple of relevant articles-one US centric and a little dated but still indicative of some of the issues.