You'll need state issued ID if you want to set foot in Belgium, EU citizen or not. You can be fined for walking around without ID. I suspect other EU countries have similarly disgusting laws.
Your point about people who can't leave their homes still stands.
Most EU countries I know have similar laws. Not sure why that is disgusting so. In Germany you have to identify yourself with a valid ID within 24 hours, if I remember well. Usually you have your ID in wallet anyways.
EDIT: As every resident has a primary residency address registered, this also serves as, what in the US would call it, voter registration. No purging, no tempering, not separate registration. You just get the papers by mail to your primary address. Works as well for EU residents for local elections.
Your point about people who can't leave their homes still stands.