But it doesn't matter if you like doing your work. If you're working all the time, to the point where you can't arrange a doctor's appointment, you're working way too much. When you're in a leadership position, it's a matter of time until it impacts the rest of the team.
The one personal task that takes a lot of time that I'd consider outsourcing would be to go to the store to pick up my prescriptions. But even that gives me a chance to reflect. It's really quite hard to imagine that it's a significant loss not having a personal assistant.
What are some tasks that need to be outsourced?
(Another way to phrase it: The rest of their team probably don't have personal assistants. If it's a work necessity, they should consider making a personal assistant a company benefit.)