Some laws are made to be broken.
In this case, in the most literal sense. Laws around sex offenders in the US are often made to be impossible to obey, in order to either force said offenders to move elsewhere (NIMBYism in action) or to provide an excuse to jail them. The best-known example of this is the colony of sex offenders formerly living under a bridge in Florida. A 'for the children' law in Miami prohibits sex offenders from living within 2500 feet of anywhere children may gather: Schools, daycare centers, homeless shelters(I don't know why), shopping malls, skating rinks, parks, even bus stops. So many that every square inch of Miami is within at least one of these exclusion zones, and so forcing sex offenders to either go underground or move to the shanty town illegally established under a bridge just outside city limits. The law wasn't made to be obeyed: It was made to be impossible to obey.
This sounds like a very similar approach. Just try registering every name you ever use on any service. Sooner or later, you're going to slip up - and if the authorities are in the habbit of following you around online and closing down all the accounts you open, it's going to be very tempting to 'forget' to report a few. Then back to jail you go, just as the writers of the law intended!