OP I am completely with you.
In his shoes I would have jumped to it and I would have seen it as an opportunity to be helpful to, and impress, someone more senior who may be supportive of me in future.
We don’t have exactly this issue - our Gen Zs would do the work if asked but nonetheless there is still a difference in attitude in some of them which makes them less proactive and less hardworking than previous generations.
We are addressing this by coaching the whole team: so we are telling them, as a group:
• yes, we do expect them to work out of hours sometimes (and sometimes very late and over weekends - they are lawyers and it’s in the contract).
• Yes, we expect them to proactive and take the initiative when there is work to progress. When they have no work, we expect them to make it clear that they have capacity and hunt some down.
• No, they should not slink off at 6pm when there is something urgent to do, or other team members are flat out/struggling, without checking in first if they are needed or they can help.
• You could add: yes, you are required to take stuff on when given to you by a senior member of the team even if not your direct line manager.
Our guys are very highly paid and this has been the industry norm for decades - I work in a high pay, high performance industry - but nonetheless over the last few years we have had to spell out these basics. Once we have done that, they do tend to improve.
The conflict comes not from a lack of ability or an inherent personality issue, but unhelpful societal conditioning which has suggested that everyone should centre themselves at all times, to assert boundaries in a very black and white way and be given constant support and explanations. There is an obvious cost to productivity (which is unhelpful to the population as a whole).
Ironically I find that once they get the message, and do properly start to muck in, they get busier and become more a part of the team - and their competence and competence visibly improves. A number of them who’ve shifted their viewpoint have said that - obviously despite not enjoying having to give up a few evenings and weekends - they find their working life much more fulfilling now that they have committed fully to it, rather than something they keep at arm’s length.