I agree that it shouldn't be altered or removed as that would remove a safe haven for civs. As some new players and old ones have Hemmit boxes the inconvenience of a crushing is drastically larger than for BlackWater, however is still a pain. If Police catch someone in the act of crimes as you suggested above you should add the charges onto their ticket without the database as you don't have their ID. However, this would still reduce the incentive to carry the ID card just in case of being caught.
While role play is a good solution to the problem with good reasoning and explanation to the officer inside of role play sometimes tickets are removed just make sure that, is instructed to officers as it is a rarity. While easier for BlackWater more people should be able to use role play as the correct way to firstly remove the ticket.
Finally, the point about manual jail time is an interesting concept as without the ID Police could charge the full amount of jail time - up to one hour - but with the ID the past crimes may be clean resulting in another role play position to remove the jail or reduce it depending on how the Officer sees it.
Overall I believe that the system should remain a feature to help support players however the jail time and charges suggestions could both have an interesting change to alter how people are dealt with.