I had a franchise that I got in 1990. I remember when I called a mentor/friend in the business the first time that I got the flu. I asked him "How do I or who do I call in sick to?" . My mentor's response was - "just contact everyone you were going to do business with today", which was about 60 people. An impossible task. I went to work sick.
Not the best job situation, but the reality if you are a sole operator.
The point is that people who are established likely can hire someone to make those calls. There is no reason you can't automate it. The new people who are getting established end up usually finding it is not worth it.
My father is a physician in private practice. He rarely takes time off for being sick but it is possible to do either in an emergency or just being very sick. His front desk people could cancel his appointments.
This is not cost free, and it is a lot harder than just calling in sick. After all if you have fixed expenses, such as salaried employees, they collect their money whether or not you work.
So it is very different. Automating some of the processes can cut down on the expenses but it is still a major thing and not really comparable.
Again, your response shows you missed the message.
The lesson wasn't about this particular set of circumstances. Of course it would be trivial to automate this specific use case. The point is that as a business owner, as the person onto who everything comes down in the end, you sometimes just have to suck it up and do what no salaried person would do. The lesson was: as an employee you can just call somebody and make your sickness their problem (I'm not suggesting that people with cancer can make that somebody else's problem, please no autistic readings of an abstract point). As the boss, the final person responsible, you have nobody to offload things like this to. You just have to find a solution and often that solution is in muscling through the obstacle.
Not the best job situation, but the reality if you are a sole operator.