Most young men in the US register to the selective service system. However, very few of them keep their contact information up to date. Selective service is aware of this flaw: http://www.sss.gov/FSadress.htm .
However, most young men either have jobs (and therefore the IRS and Social Security have contact information for them), get federal student aid (and therefore the department of education has contact information for them), or have drivers' licenses (and therefore one of the 50 states has contact information for them).
Therefore, it would be cheaper to scrap the current registration system, and replace it with the appropriate database queries. In the unlikely event of a draft, those queries will produce more accurate information.