I think you're headed in the right direction, and it sounds like you understand what I was trying to say. I'm sorry you have so many duds on your team, but you know the game, and sounds like you're acting on it.

You're absolutely right, remote workers - especially those in customer service or any on-demand platform must be available at all times. The nice thing of being at home is that you can be a bit more relaxed, but that doesn't mean shutting your computer and walking away, it means you can hear the call coming in while you're getting a cup of coffee.

Good managers aren't micromanagers like I said, but you're seeing the other side, but they will be if forced. I agree with your bosses, your specific employee you have in mind has lost work from home privileges, it's how you carry that out in your head now. Personally, I would start keeping a record of missed calls and if you have it in your company, start building a PIP. Missed calls is absolutely a metric for a customer service agent. I'm not saying anyone is a perfect 0 missed calls, but you can take the average that everyone else has (double it to be generous maybe), and then you have this person's target level. If they're consistently above that, well, there you go. PIP and then if no improvement out the door.

For the flus, well, for that one since it's health I would inform your HR team of what you suspect is happening along with the proof of the pattern and ask for guidance. They'll probably guide you on how you should proceed there so that the company doesn't come off as "not caring about health" - but they're definitely not going to be happy with an employee faking illness.

As for the rest of the team, motivation may come from that. Not saying from fear, but they probably know Kevin is over there dicking around and offline most of the time, and so it makes them think that he's just getting away with it, and demoralizes them because they probably do care about the job. I know I've been in that position before, nothing kills morale like a teammate who doesn't care at all.

I really do wish you good luck. Management isn't easy when you have a team of duds, but I've seen great managers come in and turn a team around - and a large part of that is cutting the chaff so to speak. Sounds like you know what sort of boss you like and who you want to be, and that's the boss I strive to be too, but for some people they just don't want a boss at all. And for them we have to become the bosses we hate.