To me, this is just a bit of an excuse for young people.
I know, because I was one of those young people who sometimes didn't vote when I should have done in the past.
Signing up to the Electoral register takes all in all, 3-5 minutes online. It requires absolutely no effort.
The working days argument doesn't fly. Look at this chart:
18-34 year olds have much lower turnout than 35-64 year olds.
The majority of both these age brackets are working full time. Many of the 18-24 age brackets are students. There is no reason why 55-64 year olds can reach around 80% but 18-24 can barely cross the 50% threshold.
Most democracies require voting ID.
France, Czech Republic, Finland, Brazil, Argentina, Germany (though there is some nuance here), Greece, Canada, Hungary, Iceland, India hands out photo ID's to everyone just for elections, Ireland, Israel, Luxembourg, Mexico, Netherlands, Norway, Switzerland, Sweden, USA all require photo ID in order to vote.
Australia, and formerly the UK, seem to be the only major countries that do not require a form of photo ID upon voting.
https://en.wikipedia.org/wiki/Voter_identification_laws
This gives a breakdown of each democracies rules around this.
This is definetely not the reason why young people don't vote here.