Well, if you become too sick to work for longer than that, what happens then? Surely there’s some backup. If not, you’re not always going to be able to keep that promise.
You can use software like AppogeeHR to set up vacation emails that will automatically turn on when you go away for approved leave. You can also create templates of emails to share with your team with a tool like Right Inbox.

But I also believe there’s meaningful power in the mundane cultural norms we set and practice. Email, for better or worse, makes up a large chunk of how knowledge workers communicate. So much of this communication is muddled by broken email habits and larger anxieties around performing productivity. We’re constantly nervous about asking too much of others or doing too little on behalf of our coworkers. But we’re also stuck in work patterns that force us to communicate constantly and normalize working and demanding things from colleagues at all hours.
The problem was that this had to be done on deadline and people wanted me to do other things for them that weren’t time sensitive. So I put up an internal-only out of office that basically said “hey sorry I’m working on project X and we have a tight deadline. If this isn’t urgent I’ll get back to you next week. If it is urgent, let me know!”