You don't need to work 24/7. At most jobs, you just need to seem like you work 24/7. Batch up all your emails for the day, then space them out to be sent at odd hours like 11:30pm and 5:45am using something like Boomerang for Gmail.[1] Everyone will think you're working constantly.
I work at a company that's extremely supportive of good work life balance. We offer lots of flexibility on hours, facilitate working from home, and encourage people to work at a sustainable pace.
That didn't stop one fellow, many years ago, from trying exactly this. He'd commit code that was simply reindentation/style changes, send emails, etc, late at night, in an attempt to paper over the fact that he was simply a weak contributor that produced low quality code.
Everyone saw straight through him and recognized the absurdity for what it was.
Maintain work-life balance. If the company you work for doesn't support that choice, work somewhere else. It is an absolute lie that "most jobs" need you to "seem like you work 24/7", and perpetuating that lie only makes it easier for the bad actors to justify their behaviour.
Completely agree. Was joking in my original comment. Obviously having a healthy lifestyle will lead to increased productivity. Fetishizing workaholism is dumb and a big part of why Wall Street is struggling to retain talent these days.
[1] http://www.boomeranggmail.com/