In most countries its not mandatory just the most normal and expected thing. For instance in Canada the vast majority of people vote with their government ID (note that you can also get ID for free) but those that don’t can have someone that knows them vouch for them. The UK and Australia have similar rules.

This is a pretty important exception that allows the homeless to vote (its hard to get ID when you don’t have a mailing address), those too old for administrative processes and those who have bad luck (say you get your wallet stolen on the way to the polling station).