In the US, there are fewer people who expunge criminal records because there are companies that will produced expunged records in background checks so long as they were public at any time. Banning this gets into 1st amendment grounds.
And that's the flip side: labeling theory. In places like Australia, certain crimes do get removed from your record so long as you've stayed out of the system for five years. Even their sex offender registry has limited use (certain jobs, housing restrictions etc.); it's not public like ours. Then again, they don't have freedom of speech (except in Victoria; sorta).
Could we have laws that restrict companies from considering criminal records past x number of years in the US? I'm not sure if that'd be possible in our currently legal system.
In America, you can't really restrict information, once it's published, except in certain limited cases (like when a case involves a minor).