I think it very unlikely to go anything like this far, but in extremis it would be police demanding to see your papers whenever they wished
This already happens within the EU in some countries. From personal experience I know that it happens regularly in Spain and Ireland if driving a vehicle Most of the time it is to check the car is legally on the road, but in both countries a driving license must be carried while driving so it is not unusual to be asked to show it. Other road blocks in Ireland are more thorough,involving social welfare and revenue officers as wellas the Gardaí, but are not as common. The UK is very lucky that such roadblocks are extremely rare, but ANPR has much the same impact.
Whether such checks are a good or bad thing, or if they reduce criminality, is another discussion. The reality is that such checks already exist elsewhere within the EU and are not considered onerous.