> The government could disallow access to all felony records (probably with an exemption for police)
So instead of searching government records to find out if you have been convicted of a felony when you apply to work for me, I use Google to find a newspaper report of your conviction. Not as reliable, but will still probably turn up most applicants with serious felony convictions.
If we are in one of the 40 state that does not prohibit employers from running credit checks on applicants (or if we are in one of those states but the job is one for which there is commonly an exception that allows credit checks, such as jobs in banking) [1], then I can find addresses of banks and loan providers you have used, and possibly more addresses, giving me geographical areas you have probably been in. I can do searches of the local newspapers there, which would be more likely to cover any less serious felony convictions.
Same goes for the locations of any past employers on your resume.
The internet greatly increased the difficulty of leaving your past behind. Even if the primary record (like the government record of your conviction and sentence) is blocked, you leave plenty of breadcrumbs on your way to the present, and the internet preserves them.
[1] http://www.esrcheck.com/Articles/States-with-Laws-Regulating...