You kind of can. You can gauge taking a sick day against how sick you are and if you have anything pressing at work.
I am speaking in theory, as I don't currently have a "traditional" german employer, am running a company with my partner, and can work at home. But I often think "what would i do under these circumstances if i worked for a real employer, where i HAD to be present, didn't have a deadline and I felt this way and may benefit in the longer run by taking a day off and sleeping it off? You are quite remarkable for not needing very many days off...That's impressive.
Examples include: extreme painful period (i have had many 2 days like this in my life, but I've seen family members and friends suffer quite severely). other examples: Migraines. Allergies. bleeding, bursting Hemmorhoids (I had an employee decide to come to work, then had to go home for that reason - poor thing couldnt even sit). mild Diarrhea (can work, feel ok, but releasing gas not trustworth). In many of these cases, you can make a decision: take a day off, or medicate yourself to the level of a zombie just to be "present" in the work place. All these are decisions people could make - i.e. if i have only taken 2 sick days this year, have a terrible migraine and could sleep it off rather than take a medication that has bad side effects, and i know that the average is 18 days a year, then i would take that day off. If i have already taken days off for a bad flu earlier that year, then I might consider chugging back some painkillers and bearing through it.